Speedsolving.com Wiki - User contributions [en]

Nautilus

2026-09-02T19:17:00Z

Athefre:

{| border="1" class="infobox-template" style="float: right; border-collapse:collapse; width: 22em; font-size: 90%; margin: 0 0 10px 10px;"
|
{| border="0" cellpadding="3" bgcolor="#F0F0F0" cellspacing="2" style="color:black; text-align:center; width: 100%"
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| bgcolor="#D0DFEE" colspan="2" style="font-size: 125%;" | '''{{{name|}}} Nautilus'''
|-
| colspan="2" style="font-size:90%;"| [[Image:Nautilus.png|200px]]
|-
| bgcolor="#E0E8EF" colspan="2" | '''Information'''
|-
| bgcolor="#F0F0F0" align="right" | '''Proposer:'''
| align="left" | {{{proposers|[[James Straughan|Michael James Straughan]]}}}
|-
| bgcolor="#F0F0F0" align="right" | '''Proposed:'''
| align="left" | {{{year|2006}}}
|-
| bgcolor="#F0F0F0" align="right" | '''No. Steps:'''
| align="left" | {{{steps|varies}}}
|-
| bgcolor="#F0F0F0" align="right" | '''No. Algs:'''
| align="left" | {{{algs|varies}}}
|-
| bgcolor="#F0F0F0" align="right" | '''Purpose:'''
| align="left" | {{{purpose|[[Speedsolving]]}}}
|-
|}
|}

'''Nautilus''' is a speedsolving method developed by Michael James Straughan. It was originally developed in 2006 but was re-developed with additional variants starting in 2020. The method has since become an overall concept of reaching the <U, r U r'> move group, where puzzles even outside of 3x3 have a state where the last layer is unsolved and all of the front layer pieces are unsolved except for the very left side.

== Steps ==

The idea is to build upon the [[Roux]] method by getting the DB edge solved early, leading to the rest of the solve being completely automatic and the final edge step being one-lookable without thousands of cases.

# Shell: Build a 1x2x3 at dL then build a 2x2x2 at dbr.
# Last Pair: Add the last pair at dFR.
# Corners: Solve the corners of the upper layer.
# L5E: Solve the last five edges. There are 245 cases.

'''Advantages to having DB solved'''

* Easier to recognize L5E while solving the corners versus full LSE.
* Advancements can more easily be implemented. A major complaint against the Roux method is that there are no big advancements like ZB for CFOP. With the DB edge solved, the number of edge cases is reduced and it becomes easier to combine the final steps. One thing Roux users have tried is CMLLEO, influencing EO while solving CMLL. But there are too many edge cases and poor visibility, making this complex. With Nautilus it is much easier to build an algorithm set that solves the corners and orients edges.
* The last pair is more easily tracked, recognized, and solved automatically or by using algorithms.
* Less effort to learn the 245 L5E algorithms to reach near optimal move count of 11 moves versus the 1,000 to 2,000 one look LSE cases at 11 moves or EOLRb at 13 to 13.5 moves.
* Additional move sets can more easily be implemented in the last edges step. Because L5E is algorithm based, the solver can use memorized and practiced algorithms that have the best ergonomics that don't always stick to <M, U>.
* There is no dots case or ambiguous or difficult M slice 3 cycle recognition.

[[image:Nautilus_L5E.png|300px|center]]

== Pros and Cons ==

'''Pros'''

* Great look-ahead for the rest of the solve after the primary shape is built.
* Most of the solve involves the use of only the dominant hand.
* Good for both two handed and one handed solving.
* Rotationless.
* Low move-count.

'''Cons'''

* Requires learning more algorithms compared to CFOP, Petrus, and ZZ without ZBLL, and base Roux.
* The 2x2x2 block building requires strategies not used in other methods.

== Variants ==

=== LSLL ===

# After the primary method shape, orient all edges while inserting the DF edge.
# Finish using any LSLL method.

[[image:Nautilus_LSLL.png|300px|center]]

=== LL ===

# Completely solve the empty square. This can be performed intuitively or with algorithms. If all edges are oriented, there are 116 algorithms that average 8 moves. When edges aren't oriented, there are 467 algorithms.
# Solve the last layer using any variant.

[[image:Nautilus_LL.png|300px|center]]

== Adaptions to Other Puzzles ==

The Nautilus concept of <U, r U r'> solving is easily adaptable to many puzzles. Below are some of the puzzles for which Nautilus has been developed.

=== FTO ===

[[Nautilus (FTO)|Nautilus FTO wiki page]]

[[image:NautilusLL-2.png|300px|center]]

=== Square-1 ===

Ryan Hudgens (OreKehStrah) adapted Nautilus to Square-1. [https://docs.google.com/spreadsheets/d/1DBdLGCWmVlNifwtq8ijIb_Rjim9IK9PC62YxrLCpQ3U/edit?usp=sharing Ryan Hudgens' Nautilus Square-1 guide]

[[image:NautilusSquare-1.png|300px|center]]

=== Big Cubes ===

[https://sites.google.com/site/athefre/other-puzzles/nautilus-big-cubes Webpage for using Nautilus on big cubes]

[[image:NautilusBigCubes.png|300px|center]]

== History ==

In 2006, the [[MI1]] method was developed. The primary shape in that method was very close to the one in Nautilus. The only difference being that the DR edge wasn't solved. It was found that having the DR edge slot be empty caused problems for ergonomics. So that same year it was decided to solve the DR edge along with the rest of the shape and branch Nautilus off into its own method. This produced much better ergonomics and led to better variants. In 2020 new, more advanced variants were added to the method.

== External Links ==
* [https://sites.google.com/view/nautilus-method Website]
* [https://discord.gg/eV2Tm3Qc3k Nautilus Discord Server]

[[Category:3x3x3 methods]]
[[Category:3x3x3 speedsolving methods]]
[[Category:Acronyms]]

File:NautilusBigCubes.png

2026-09-02T19:10:48Z

Athefre:

File:NautilusSquare-1.png

2026-09-02T19:10:07Z

Athefre:

Nautilus (FTO)

2026-08-31T22:43:30Z

Athefre:

{| border="1" class="infobox-template" style="float: right; border-collapse:collapse; width: 22em; font-size: 90%; margin: 0 0 10px 10px;"
|
{| border="0" cellpadding="3" bgcolor="#F0F0F0" cellspacing="2" style="color:black; text-align:center; width: 100%"
|-
| bgcolor="#D0DFEE" colspan="2" style="font-size: 125%;" | '''{{{name|}}} Nautilus (FTO)'''
|-
| colspan="2" style="font-size:90%;"| [[Image:NautilusLL-2.png|200px]]
|-
| bgcolor="#E0E8EF" colspan="2" | '''Information'''
|-
| bgcolor="#F0F0F0" align="right" | '''Proposer:'''
| align="left" | {{{proposers|[[James Straughan]]}}}
|-
| bgcolor="#F0F0F0" align="right" | '''Developers:'''
| align="left" | {{{proposers|[[James Straughan]], [[Liam Highducheck]], [[Vincent Trang]], [[Malte Ihlefeld]], [[Ryan Hudgens]]}}}
|-
| bgcolor="#F0F0F0" align="right" | '''Proposed:'''
| align="left" | {{{year|2024}}}
|-
| bgcolor="#F0F0F0" align="right" | '''No. Steps:'''
| align="left" | {{{steps|varies}}}
|-
| bgcolor="#F0F0F0" align="right" | '''No. Algs:'''
| align="left" | {{{algs|varies}}}
|-
| bgcolor="#F0F0F0" align="right" | '''Purpose:'''
| align="left" | {{{purpose|[[Speedsolving]]}}}
|-
|}
|}

'''Nautilus''' is a [[Face Turning Octahedron]] speedsolving method developed by James Straughan with assistance from Liam Highducheck and Vincent Trang. The method has a focus on simple, automatic, and algorithm based solving similar to [[CFOP]] for 3x3.

== Steps ==

'''1. First Block:''' Solve the BL layer minus the corner and two small triangle centers of the U layer. This step is typically solved by first building the large center on BL then adding two triples (a corner and two attached triangles). Another good start is an arrow block, which is the large center plus a triple, then adding the final triple.
[[image:NautilusFTOFB-2.png|300px|center]]
'''2. Centers:''' Solve the U, F and BR large centers. Solving any two of these automatically solves the third.
[[image:NautilusCenters-2.png|300px|center]]
'''3. Last Triple:''' Complete the F2L by solving the final corner and two triangles. This step can be solved in a single step using algorithms or broken down into two or three steps for more basic solving.
[[image:NautilusLastTriple-2.png|300px|center]]
'''4. Last Layer:''' Solve the last layer. The standard steps are to solve the side triangles in one step then solve the corners in the second step. Or, 1LLL can be used, which consists of 377 cases. The advantage to ending with a last layer is that recognition is simple. Only the sides of the layer need to be checked to determine a case, similar to 2 sided PLL recognition. There is no need to check the U face or any other pieces around the FTO.
[[image:NautilusLL-2.png|300px|center]]

== Pros ==

* Simple, automatic steps.
* Algorithm based solving may be faster than intuitive based methods.
* Last layer recognition is simple, requiring only checking the sides of the last layer.

== Cons ==

* Large number of algorithms to learn if learning 1LLL.

== Advancements ==

=== 1LLL ===

At just 377 algorithms, 1LLL in combination with a one step last F2L triple provides a very fast two step finish to the method.

=== Advanced Last Slot ===

An alternate ending to solving the first two layers is to solve to the F2L-1 equivalent. This leaves a large F2L "pair" that can be solved in a single step. This creates a more advanced two step ending of solving the large pair then 1LLL. The large pair consists of everything except for the right two triangles of the F layer, the edge, the bottom right side triangle, and the corner.

=== Early Corner Orientation ===

The ZBLS equivalent would be to orient the last layer corners during a previous step. This can be accomplished during the last triple step or integrated into the advanced last slot.

=== Four Triples ===

Another possible advancement is to construct four triples at the last triple step. Then solve the four triples. [[Vincent Trang]] developed an intuitive technique for building the triples, but the technique hasn't been perfected. There is also the possibility of building the triples using algorithms, maybe even through integrating a technique similar to [[CLL+1]]. However, the recognition and execution speed hasn't been tested to compare it to the more automated and algorithm based steps currently used.

== Last Layer Variants ==

Other last layer ideas have been proposed:

* Orient the last layer corners then use PLL.
* Solve the three corners then the last six triangles.
* Form the three triples on the last layer in any orientation then solve the triples.
* Orient the last layer corners while solving the last six triangles relative to the corners. This forms three triples that can then be permuted using one of two algorithms. This idea was proposed by Vincent Trang.
* Leave out the bottom right corner and solve all triangles. Then solve the final four corners in a single step.
* Solve one triple in one algorithm then solve the other two corners and four triangles of the last layer in one algorithm.
* Solve two triangles of the last layer then solve the remaining pieces.

== External Links ==
* [https://www.nautilusfto.com/ Official Website]
* [https://discord.gg/GJB2ER2Q3M Discord Server]
* [https://docs.google.com/spreadsheets/d/1NSa4MMV10ma4nNJKRfET_M1OwxULN_oSWUkThwLcTh0/edit?gid=323120253#gid=323120253 Last Triple Algorithms]
* [https://docs.google.com/spreadsheets/d/1Dh4MEQzpCuTylqnkn09UxBEvEq9MNYMqMiWQgFsBuYE/edit?gid=2102380954#gid=2102380954 2 Look Last Layer Algorithms]
* [https://docs.google.com/spreadsheets/d/15v0A0PipO8RcEeS7TFAaAv3dI1zBykaopkXQK_WnLo0/edit?gid=1497905026#gid=1497905026 1LLL Algorithms]

[[Category:Acronyms]]

Face Turning Octahedron

2026-08-31T22:43:06Z

Athefre:

{{Puzzle Infobox|
|NAME=Face Turning Octahedron
|IMAGE=Dayan-fto-magnetic-ball-core-stickerless_540x.webp
|ALTERNATIVENAMES=FTO
|MECHANISM=Face Turning Octahedron
|SHAPE=Octahedron
|INVENTOR=David Pitcher
|YEAR=c. 2003
|COMPANIES=[[Dayan]], [[DianSheng]], [[LanLan]], [[Shengshou]], [[Qiyi]], [[Maru]]
|JAAPSCH=octaface}}

The Face Turning Octahedron is a three-layered face turning octahedral puzzle for which all three layers are the same width. The first working version was made by David Pitcher in the early 2000s and was later mass-produced by [[LanLan]]. In 2024, [[DianSheng]] released a magnetic version, which was followed by other speed versions by various companies including [[Dayan]], [[Qiyi]], and [[Shengshou]]. Before these versions were mass-produced, it was common to make one by attaching printed extentions to a Qiyi [[Rex Cube]].

== Basic Characteristics ==
The Face Turning Octahedron is a face-turning regular octahedral puzzle with a cut depth such that the cuts intersect at a point in the center of each face. It is the second shallowest possible planar cut depth of a face-turning octahedral puzzle (with the shallowest being the Dino Octahedron). Its pieces consist of 6 corners, 12 edges, and 24 X-centers. Since rotation about the faces of an octahedron result in two distinct sets of four faces each where a face from one set can never reach the starting position of any face from the other set, the stickers of an FTO are divided into two distinct orbits, where colors of adjacent faces can never end up on the same face. This means that the corners only have two possible orientations per location (when the puzzle is scrambled without cube rotations), the edges are always oriented, and there are two sets of X-centers that never mix. Interestingly, this also means than an FTO stickered with only four colors, with opposite sides having the same color, solves exactly the same way as an FTO stickered with all eight colors.

The corners turn out to be equivalent to pyraminx edges, which means that only even permutations are possible and that a single corner "flip" is impossible. Additionally, since each face turn does a 3-cycle of edges, only even permutations are possible for edges as well.

As calculated by Jaap, the FTO has a total of 31,408,133,379,194,880,000,000 visually distinct positions [https://www.jaapsch.net/puzzles/octaface.htm].

If the X-centers are to be each considered unique, then the number becomes [(6!/2)(2^6/2)(12!/2)(12!/2)^2]/12 = 13,188,400,838,457,446,891,520,000,000 total positions.

== Related Puzzles ==

=== Skewb Diamond ===

{{Main Article|Article=Skewb Diamond}}

[[Image:Skewb_diamond.png|120px]]

The Skewb Diamond, also known as the 2x2 FTO, can be seen as either a face-turning octahedron with deep cuts or a 2-layer version of the standard FTO. It is also an octahedral shape transformation of a [[Skewb]] where the Skewb's centers correspond to the Skewb Diamond's corners and the Skewb's corners correspond to the Skewb Diamond's centers, which means that orientation matters on the opposite pieces as compared to the standard Skewb.

=== Master FTO ===

[[Image:masterfto.png|120px]]

The Master FTO, or 4x4 FTO, is a four-layered face-turning octahedron with two different cut depths (one deep and one shallow) such that the faces appear like those of a [[Master Pyraminx]].

=== Other Related Puzzles ===

There are four distinct face-turning octahedral puzzles that each have a single planar cut depth. From shallowest to deepest, they are the Dino Octahedron, the standard FTO (the main subject of this article), the Master Skewb Diamond, and the Skewb Diamond (discussed above). The Dino Octahedron, briefly produced by MF8, is the shallowest possible face-turning octahedron with one cut per side. It is equivalent to a standard FTO with the addition of fixed centers. The Master Skewb Diamond is a face-turning octahedral puzzle with a cut depth between the standard FTO and the Skewb Diamond, and can be seen as a shape transformation of the Master Skewb. Although it has not yet been mass-produced in its pure form, MF8 has made a "crazy" version with added circular cuts on the faces. The only functional difference between the Dino Octahedron and the Master Skewb Diamond is that the centers are fixed on the Dino Octahedron, whereas they turn with the faces on the Master Skewb Diamond.

== Methods ==

There are many methods used to solve the Face Turning Octahedron, the most popular of which are described below.

=== Bencisco ===

The [[Bencisco method]] is a method based on ending in a step called Last Three Triples and was created by Ben Streeter in 2020.

# First Block: Solve a block on the BL layer consisting of a large hexagon center and two triples. A triple is a corner and two opposite small triangle centers.
# Centers: Solve the remaining three hexagon centers in the layers to the right of the block built in the first step.
# Triple: Rotate to have the upper left corner be at the bottom and solve the unsolved triple at that position.
# Last Three Triples: Middle layer center triangles, last layer center triangles, and last layer corners remain to be solved. Finish the solve by forming three triples then solving them to their correct positions, or solve everything in a single step using 179 algorithms.

=== Nautilus ===

The [[Nautilus (FTO)|Nautilus method]] is an F2L and Last Layer method that was developed by a team consisting of [[James Straughan]], Liam Highducheck, Vincent Trang, and Malte Ihlefeld, with additional input by Ryan Hudgens and mrmangohands.

# First Block: Solve a block on the BL layer consisting of a large hexagon center and two triples.
# Centers: Solve the remaining three hexagon centers.
# Triple: Solve the last triple at the bottom right, completing the first two layers.
# Last Layer: Solve the last layer. This is typically accomplished by first solving the center triangles then the corners. 1LLL has also been developed.

There are some alternative steps to solving the first two layers that users may prefer:

# First Block: Solve a block on the BL layer consisting of a large hexagon center and two triples.
# Stripe: Solve the F2L stripe to the right of the first block. This leaves just the U and R layers unsolved.
# F2L: Solve the remainder of the F2L using just U and R turns.
# Last Layer: Solve the last layer.

=== Vertigo ===

By Ryan Hudgens and Ben Streeter.

# Vertex: Solve a corner and its surrounding four triangles and four edges.
# Second Vertex: Solve another vertex adjacent to the first. Keep these two at the bottom left of the first two layers.
# Edges and Triangles: Solve the last four edges and the two triangles at either the intersection of DR or UL.
# Last Six Triangles: If in the last step the two triangles at DR were solved, solve the three remaining U face triangles and the three that belong in the middle layer beneath the U layer, equivalent to the E layer on 3x3. Do the opposite of this if in the last step the two triangles at UL were solved.
# Last Three Triples: Finish the solve by forming the last three triples then solving them to their correct positions, or solve everything in a single step using 179 algorithms.

=== CFL ===

CFL is a method similar to CFOP and was created by James Straughan.

# Centers: Solve the three large hexagon centers around the sides of the first two layers.
# F2L: Solve the three triples of the first two layers.
# Last Layer: Solve the last layer. This is typically accomplished by first solving the triangle centers then the corners, but other systems also exist such as OLL then PLL or 1LLL.

Many CFOP techniques can be carried over such as pseudo slotting, edge control (corner control or triangle control in CFL), ZBLS (orienting corners or positioning triangles during the last slot), and XCross (arrow block + centers in CFL).

=== L4T Redux ===

A version of reduction that combines modern techniques with reduction to Pyraminx steps. All of the various Pyraminx steps can be incorporated into the method. The method was developed by Vincent Trang, with some algorithm development and an EIF version proposal by James Straughan.

# First Block: Solve a block on the BL layer consisting of a large hexagon center and two triples. The two triples can be any triple and not just the ones that belong in those positions. This allows for more freedom in the reduction step.
# Centers: Solve the remaining three hexagon centers.
# Reduction: Form the last four triples using big cube style slicing techniques. This reduces the FTO to a Pyraminx stage.
# Pyra Stage: Solve as a Pyraminx.

It is also possible to perform reduction in an edge in front grip. The R layer center and a triangular first block on BL would be solved first, then the remainder of the middle slice of the first two layers leaving out the bottom triangle. This allows for a U R r pairing move group that doesn't break the R layer center. Reduction would be performed using r turns to attach triangles, then pairs and triples are easily moved around using U and R turns.

=== Julian ===

# Center: Solve a large hexagon center.
# Arrow Blocks: Add two adjacent arrow blocks to the hexagon center.
# Third arrow: Solve the last arrow connected to the hexagon center, but leave out the two triangles that would go around the sides of the layer where the hexagon center is.
# Corners: Solve the last three corners.
# Triangles: Use commutators to solve all remaining small triangle centers.

=== Other F2L Methods ===

Two of the mentioned methods, Nautilus and CFL, involve solving F2L then the last layer. Various 3x3 methods can be adapted to FTO to solve the first two layers [https://sites.google.com/site/athefre/other-puzzles/fto-f2l-methods]. Some of these involve solving F2L from an edge in front perspective, which involves solving a right layer center and left layer block, similar to many big cube methods. This perspective allows for U R r turning that doesn't disturb the built right layer center.

==== LEOR (CIF) ====

# First Block: Solve a block on the BL layer consisting of a large hexagon center and two triples.
# Stripe: Solve the F2L stripe to the right of the first block. This leaves just the U and R layers unsolved.
# F2L: Solve the remainder of the F2L using just U and R turns.
# Last Layer: Solve the last layer.

==== LEOR (EIF) ====

# First Block + Center: Solve the R layer center and a block on the BL layer consisting of a half center and its two outer triangles and a triple on the bottom. This leaves the U layer, R layer triples, and the slice layer between the R and BL layers unsolved.
# Stripe: Solve the F2L stripe between the first block and R layer center.
# F2L: Solve the two remaining F2L triples.
# Last Layer: Solve the last layer.

==== Nautilus (EIF) ====

# First Block + Center: Solve the R layer center and a block on the BL layer consisting of a half center and its two outer triangles and a triple on the bottom. This leaves the U layer, R layer triples, and the slice layer between the R and BL layers unsolved.
# Pyramid: Build a 2x2x2 pyramid on the bottom in the back.
# Stripe: Finish the stripe between the first block and R layer center.
# Last Slot: Solve the last slot, which is the triple on the bottom in the front.
# Last Layer: Solve the last layer.

== Tutorials/Guides ==
* [https://www.youtube.com/watch?v=6JT2tU00ccs Bencisco guide]
* [https://www.nautilusfto.com/ Nautilus website]
* [https://sites.google.com/site/athefre/other-puzzles/cfl?authuser=0 CFL website]
* [https://docs.google.com/document/d/18CMTrFC9PYkEsheOHnywzvV0EdCb3SFGQXSK0DDb30o/edit?pli=1&tab=t.0 L4T Redux guide]
* [https://docs.google.com/spreadsheets/d/1_IHL077w-9U-qtpF9hvC6CrUn7etua5QgPH8vEMqK58/edit?usp=sharing L4T Redux L4E]

[[Category:Twisty puzzles]]

Face Turning Octahedron

2026-08-27T00:50:58Z

Athefre:

{{Puzzle Infobox|
|NAME=Face Turning Octahedron
|IMAGE=Dayan-fto-magnetic-ball-core-stickerless_540x.webp
|ALTERNATIVENAMES=FTO
|MECHANISM=Face Turning Octahedron
|SHAPE=Octahedron
|INVENTOR=David Pitcher
|YEAR=c. 2003
|COMPANIES=[[Dayan]], [[DianSheng]], [[LanLan]], [[Shengshou]], [[Qiyi]], [[Maru]]
|JAAPSCH=octaface}}

The Face Turning Octahedron is a three-layered face turning octahedral puzzle for which all three layers are the same width. The first working version was made by David Pitcher in the early 2000s and was later mass-produced by [[LanLan]]. In 2024, [[DianSheng]] released a magnetic version, which was followed by other speed versions by various companies including [[Dayan]], [[Qiyi]], and [[Shengshou]]. Before these versions were mass-produced, it was common to make one by attaching printed extentions to a Qiyi [[Rex Cube]].

== Basic Characteristics ==
The Face Turning Octahedron is a face-turning regular octahedral puzzle with a cut depth such that the cuts intersect at a point in the center of each face. It is the second shallowest possible planar cut depth of a face-turning octahedral puzzle (with the shallowest being the Dino Octahedron). Its pieces consist of 6 corners, 12 edges, and 24 X-centers. Since rotation about the faces of an octahedron result in two distinct sets of four faces each where a face from one set can never reach the starting position of any face from the other set, the stickers of an FTO are divided into two distinct orbits, where colors of adjacent faces can never end up on the same face. This means that the corners only have two possible orientations per location (when the puzzle is scrambled without cube rotations), the edges are always oriented, and there are two sets of X-centers that never mix. Interestingly, this also means than an FTO stickered with only four colors, with opposite sides having the same color, solves exactly the same way as an FTO stickered with all eight colors.

The corners turn out to be equivalent to pyraminx edges, which means that only even permutations are possible and that a single corner "flip" is impossible. Additionally, since each face turn does a 3-cycle of edges, only even permutations are possible for edges as well.

As calculated by Jaap, the FTO has a total of 31,408,133,379,194,880,000,000 visually distinct positions [https://www.jaapsch.net/puzzles/octaface.htm].

If the X-centers are to be each considered unique, then the number becomes [(6!/2)(2^6/2)(12!/2)(12!/2)^2]/12 = 13,188,400,838,457,446,891,520,000,000 total positions.

== Related Puzzles ==

=== Skewb Diamond ===

{{Main Article|Article=Skewb Diamond}}

[[Image:Skewb_diamond.png|120px]]

The Skewb Diamond, also known as the 2x2 FTO, can be seen as either a face-turning octahedron with deep cuts or a 2-layer version of the standard FTO. It is also an octahedral shape transformation of a [[Skewb]] where the Skewb's centers correspond to the Skewb Diamond's corners and the Skewb's corners correspond to the Skewb Diamond's centers, which means that orientation matters on the opposite pieces as compared to the standard Skewb.

=== Master FTO ===

[[Image:masterfto.png|120px]]

The Master FTO, or 4x4 FTO, is a four-layered face-turning octahedron with two different cut depths (one deep and one shallow) such that the faces appear like those of a [[Master Pyraminx]].

=== Other Related Puzzles ===

There are four distinct face-turning octahedral puzzles that each have a single planar cut depth. From shallowest to deepest, they are the Dino Octahedron, the standard FTO (the main subject of this article), the Master Skewb Diamond, and the Skewb Diamond (discussed above). The Dino Octahedron, briefly produced by MF8, is the shallowest possible face-turning octahedron with one cut per side. It is equivalent to a standard FTO with the addition of fixed centers. The Master Skewb Diamond is a face-turning octahedral puzzle with a cut depth between the standard FTO and the Skewb Diamond, and can be seen as a shape transformation of the Master Skewb. Although it has not yet been mass-produced in its pure form, MF8 has made a "crazy" version with added circular cuts on the faces. The only functional difference between the Dino Octahedron and the Master Skewb Diamond is that the centers are fixed on the Dino Octahedron, whereas they turn with the faces on the Master Skewb Diamond.

== Methods ==

There are many methods used to solve the Face Turning Octahedron, the most popular of which are described below.

=== Bencisco ===

The [[Bencisco method]] is a method based on ending in a step called Last Three Triples and was created by Ben Streeter in 2020.

# First Block: Solve a block on the BL layer consisting of a large hexagon center and two triples. A triple is a corner and two opposite small triangle centers.
# Centers: Solve the remaining three hexagon centers in the layers to the right of the block built in the first step.
# Triple: Rotate to have the upper left corner be at the bottom and solve the unsolved triple at that position.
# Last Three Triples: Middle layer center triangles, last layer center triangles, and last layer corners remain to be solved. Finish the solve by forming three triples then solving them to their correct positions, or solve everything in a single step using 179 algorithms.

=== Nautilus ===

The [[Nautilus (FTO)|Nautilus method]] is an F2L and Last Layer method that was developed by a team consisting of [[James Straughan]], Liam Highducheck, and Vincent Trang, with additional input by Ryan Hudgens and mrmangohands.

# First Block: Solve a block on the BL layer consisting of a large hexagon center and two triples.
# Centers: Solve the remaining three hexagon centers.
# Triple: Solve the last triple at the bottom right, completing the first two layers.
# Last Layer: Solve the last layer. This is typically accomplished by first solving the center triangles then the corners. 1LLL has also been developed.

There are some alternative steps to solving the first two layers that users may prefer:

# First Block: Solve a block on the BL layer consisting of a large hexagon center and two triples.
# Stripe: Solve the F2L stripe to the right of the first block. This leaves just the U and R layers unsolved.
# F2L: Solve the remainder of the F2L using just U and R turns.
# Last Layer: Solve the last layer.

=== Vertigo ===

By Ryan Hudgens and Ben Streeter.

# Vertex: Solve a corner and its surrounding four triangles and four edges.
# Second Vertex: Solve another vertex adjacent to the first. Keep these two at the bottom left of the first two layers.
# Edges and Triangles: Solve the last four edges and the two triangles at either the intersection of DR or UL.
# Last Six Triangles: If in the last step the two triangles at DR were solved, solve the three remaining U face triangles and the three that belong in the middle layer beneath the U layer, equivalent to the E layer on 3x3. Do the opposite of this if in the last step the two triangles at UL were solved.
# Last Three Triples: Finish the solve by forming the last three triples then solving them to their correct positions, or solve everything in a single step using 179 algorithms.

=== CFL ===

CFL is a method similar to CFOP and was created by James Straughan.

# Centers: Solve the three large hexagon centers around the sides of the first two layers.
# F2L: Solve the three triples of the first two layers.
# Last Layer: Solve the last layer. This is typically accomplished by first solving the triangle centers then the corners, but other systems also exist such as OLL then PLL or 1LLL.

Many CFOP techniques can be carried over such as pseudo slotting, edge control (corner control or triangle control in CFL), ZBLS (orienting corners or positioning triangles during the last slot), and XCross (arrow block + centers in CFL).

=== L4T Redux ===

A version of reduction that combines modern techniques with reduction to Pyraminx steps. All of the various Pyraminx steps can be incorporated into the method. The method was developed by Vincent Trang, with some algorithm development and an EIF version proposal by James Straughan.

# First Block: Solve a block on the BL layer consisting of a large hexagon center and two triples. The two triples can be any triple and not just the ones that belong in those positions. This allows for more freedom in the reduction step.
# Centers: Solve the remaining three hexagon centers.
# Reduction: Form the last four triples using big cube style slicing techniques. This reduces the FTO to a Pyraminx stage.
# Pyra Stage: Solve as a Pyraminx.

It is also possible to perform reduction in an edge in front grip. The R layer center and a triangular first block on BL would be solved first, then the remainder of the middle slice of the first two layers leaving out the bottom triangle. This allows for a U R r pairing move group that doesn't break the R layer center. Reduction would be performed using r turns to attach triangles, then pairs and triples are easily moved around using U and R turns.

=== Julian ===

# Center: Solve a large hexagon center.
# Arrow Blocks: Add two adjacent arrow blocks to the hexagon center.
# Third arrow: Solve the last arrow connected to the hexagon center, but leave out the two triangles that would go around the sides of the layer where the hexagon center is.
# Corners: Solve the last three corners.
# Triangles: Use commutators to solve all remaining small triangle centers.

=== Other F2L Methods ===

Two of the mentioned methods, Nautilus and CFL, involve solving F2L then the last layer. Various 3x3 methods can be adapted to FTO to solve the first two layers [https://sites.google.com/site/athefre/other-puzzles/fto-f2l-methods]. Some of these involve solving F2L from an edge in front perspective, which involves solving a right layer center and left layer block, similar to many big cube methods. This perspective allows for U R r turning that doesn't disturb the built right layer center.

==== LEOR (CIF) ====

# First Block: Solve a block on the BL layer consisting of a large hexagon center and two triples.
# Stripe: Solve the F2L stripe to the right of the first block. This leaves just the U and R layers unsolved.
# F2L: Solve the remainder of the F2L using just U and R turns.
# Last Layer: Solve the last layer.

==== LEOR (EIF) ====

# First Block + Center: Solve the R layer center and a block on the BL layer consisting of a half center and its two outer triangles and a triple on the bottom. This leaves the U layer, R layer triples, and the slice layer between the R and BL layers unsolved.
# Stripe: Solve the F2L stripe between the first block and R layer center.
# F2L: Solve the two remaining F2L triples.
# Last Layer: Solve the last layer.

==== Nautilus (EIF) ====

# First Block + Center: Solve the R layer center and a block on the BL layer consisting of a half center and its two outer triangles and a triple on the bottom. This leaves the U layer, R layer triples, and the slice layer between the R and BL layers unsolved.
# Pyramid: Build a 2x2x2 pyramid on the bottom in the back.
# Stripe: Finish the stripe between the first block and R layer center.
# Last Slot: Solve the last slot, which is the triple on the bottom in the front.
# Last Layer: Solve the last layer.

== Tutorials/Guides ==
* [https://www.youtube.com/watch?v=6JT2tU00ccs Bencisco guide]
* [https://sites.google.com/view/nautilusfto Nautilus website]
* [https://sites.google.com/site/athefre/other-puzzles/cfl?authuser=0 CFL website]
* [https://docs.google.com/document/d/18CMTrFC9PYkEsheOHnywzvV0EdCb3SFGQXSK0DDb30o/edit?pli=1&tab=t.0 L4T Redux guide]
* [https://docs.google.com/spreadsheets/d/1_IHL077w-9U-qtpF9hvC6CrUn7etua5QgPH8vEMqK58/edit?usp=sharing L4T Redux L4E]

[[Category:Twisty puzzles]]

Nautilus (FTO)

2026-08-20T19:06:38Z

Athefre:

{| border="1" class="infobox-template" style="float: right; border-collapse:collapse; width: 22em; font-size: 90%; margin: 0 0 10px 10px;"
|
{| border="0" cellpadding="3" bgcolor="#F0F0F0" cellspacing="2" style="color:black; text-align:center; width: 100%"
|-
| bgcolor="#D0DFEE" colspan="2" style="font-size: 125%;" | '''{{{name|}}} Nautilus (FTO)'''
|-
| colspan="2" style="font-size:90%;"| [[Image:NautilusLL-2.png|200px]]
|-
| bgcolor="#E0E8EF" colspan="2" | '''Information'''
|-
| bgcolor="#F0F0F0" align="right" | '''Proposer:'''
| align="left" | {{{proposers|[[James Straughan]]}}}
|-
| bgcolor="#F0F0F0" align="right" | '''Developers:'''
| align="left" | {{{proposers|[[James Straughan]], [[Liam Highducheck]], [[Vincent Trang]], [[Malte Ihlefeld]], [[Ryan Hudgens]]}}}
|-
| bgcolor="#F0F0F0" align="right" | '''Proposed:'''
| align="left" | {{{year|2024}}}
|-
| bgcolor="#F0F0F0" align="right" | '''No. Steps:'''
| align="left" | {{{steps|varies}}}
|-
| bgcolor="#F0F0F0" align="right" | '''No. Algs:'''
| align="left" | {{{algs|varies}}}
|-
| bgcolor="#F0F0F0" align="right" | '''Purpose:'''
| align="left" | {{{purpose|[[Speedsolving]]}}}
|-
|}
|}

'''Nautilus''' is a [[Face Turning Octahedron]] speedsolving method developed by James Straughan with assistance from Liam Highducheck and Vincent Trang. The method has a focus on simple, automatic, and algorithm based solving similar to [[CFOP]] for 3x3.

== Steps ==

'''1. First Block:''' Solve the BL layer minus the corner and two small triangle centers of the U layer. This step is typically solved by first building the large center on BL then adding two triples (a corner and two attached triangles). Another good start is an arrow block, which is the large center plus a triple, then adding the final triple.
[[image:NautilusFTOFB-2.png|300px|center]]
'''2. Centers:''' Solve the U, F and BR large centers. Solving any two of these automatically solves the third.
[[image:NautilusCenters-2.png|300px|center]]
'''3. Last Triple:''' Complete the F2L by solving the final corner and two triangles. This step can be solved in a single step using algorithms or broken down into two or three steps for more basic solving.
[[image:NautilusLastTriple-2.png|300px|center]]
'''4. Last Layer:''' Solve the last layer. The standard steps are to solve the side triangles in one step then solve the corners in the second step. Or, 1LLL can be used, which consists of 377 cases. The advantage to ending with a last layer is that recognition is simple. Only the sides of the layer need to be checked to determine a case, similar to 2 sided PLL recognition. There is no need to check the U face or any other pieces around the FTO.
[[image:NautilusLL-2.png|300px|center]]

== Pros ==

* Simple, automatic steps.
* Algorithm based solving may be faster than intuitive based methods.
* Last layer recognition is simple, requiring only checking the sides of the last layer.

== Cons ==

* Large number of algorithms to learn if learning 1LLL.

== Advancements ==

=== 1LLL ===

At just 377 algorithms, 1LLL in combination with a one step last F2L triple provides a very fast two step finish to the method.

=== Advanced Last Slot ===

An alternate ending to solving the first two layers is to solve to the F2L-1 equivalent. This leaves a large F2L "pair" that can be solved in a single step. This creates a more advanced two step ending of solving the large pair then 1LLL. The large pair consists of everything except for the right two triangles of the F layer, the edge, the bottom right side triangle, and the corner.

=== Early Corner Orientation ===

The ZBLS equivalent would be to orient the last layer corners during a previous step. This can be accomplished during the last triple step or integrated into the advanced last slot.

=== Four Triples ===

Another possible advancement is to construct four triples at the last triple step. Then solve the four triples. [[Vincent Trang]] developed an intuitive technique for building the triples, but the technique hasn't been perfected. There is also the possibility of building the triples using algorithms, maybe even through integrating a technique similar to [[CLL+1]]. However, the recognition and execution speed hasn't been tested to compare it to the more automated and algorithm based steps currently used.

== Last Layer Variants ==

Other last layer ideas have been proposed:

* Orient the last layer corners then use PLL.
* Solve the three corners then the last six triangles.
* Form the three triples on the last layer in any orientation then solve the triples.
* Orient the last layer corners while solving the last six triangles relative to the corners. This forms three triples that can then be permuted using one of two algorithms. This idea was proposed by Vincent Trang.
* Leave out the bottom right corner and solve all triangles. Then solve the final four corners in a single step.
* Solve one triple in one algorithm then solve the other two corners and four triangles of the last layer in one algorithm.
* Solve two triangles of the last layer then solve the remaining pieces.

== External Links ==
* [https://sites.google.com/view/nautilusfto Official Website]
* [https://discord.gg/GJB2ER2Q3M Discord Server]
* [https://docs.google.com/spreadsheets/d/1NSa4MMV10ma4nNJKRfET_M1OwxULN_oSWUkThwLcTh0/edit?gid=323120253#gid=323120253 Last Triple Algorithms]
* [https://docs.google.com/spreadsheets/d/1Dh4MEQzpCuTylqnkn09UxBEvEq9MNYMqMiWQgFsBuYE/edit?gid=2102380954#gid=2102380954 2 Look Last Layer Algorithms]
* [https://docs.google.com/spreadsheets/d/15v0A0PipO8RcEeS7TFAaAv3dI1zBykaopkXQK_WnLo0/edit?gid=1497905026#gid=1497905026 1LLL Algorithms]

[[Category:Acronyms]]

File:NautilusLL-2.png

2026-08-20T19:01:52Z

Athefre:

File:NautilusLastTriple-2.png

2026-08-20T19:01:28Z

Athefre:

File:NautilusCenters-2.png

2026-08-20T19:00:58Z

Athefre:

File:NautilusFTOFB-2.png

2026-08-20T19:00:28Z

Athefre:

Face Turning Octahedron

2026-08-20T18:20:03Z

Athefre:

{{Puzzle Infobox|
|NAME=Face Turning Octahedron
|IMAGE=Dayan-fto-magnetic-ball-core-stickerless_540x.webp
|ALTERNATIVENAMES=FTO
|MECHANISM=Face Turning Octahedron
|SHAPE=Octahedron
|INVENTOR=David Pitcher
|YEAR=c. 2003
|COMPANIES=[[Dayan]], [[DianSheng]], [[LanLan]], [[Shengshou]], [[Qiyi]], [[Maru]]
|JAAPSCH=octaface}}

The Face Turning Octahedron is a three-layered face turning octahedral puzzle for which all three layers are the same width. The first working version was made by David Pitcher in the early 2000s and was later mass-produced by [[LanLan]]. In 2024, [[DianSheng]] released a magnetic version, which was followed by other speed versions by various companies including [[Dayan]], [[Qiyi]], and [[Shengshou]]. Before these versions were mass-produced, it was common to make one by attaching printed extentions to a Qiyi [[Rex Cube]].

== Basic Characteristics ==
The Face Turning Octahedron is a face-turning regular octahedral puzzle with a cut depth such that the cuts intersect at a point in the center of each face. It is the second shallowest possible planar cut depth of a face-turning octahedral puzzle (with the shallowest being the Dino Octahedron). Its pieces consist of 6 corners, 12 edges, and 24 X-centers. Since rotation about the faces of an octahedron result in two distinct sets of four faces each where a face from one set can never reach the starting position of any face from the other set, the stickers of an FTO are divided into two distinct orbits, where colors of adjacent faces can never end up on the same face. This means that the corners only have two possible orientations per location (when the puzzle is scrambled without cube rotations), the edges are always oriented, and there are two sets of X-centers that never mix. Interestingly, this also means than an FTO stickered with only four colors, with opposite sides having the same color, solves exactly the same way as an FTO stickered with all eight colors.

The corners turn out to be equivalent to pyraminx edges, which means that only even permutations are possible and that a single corner "flip" is impossible. Additionally, since each face turn does a 3-cycle of edges, only even permutations are possible for edges as well.

As calculated by Jaap, the FTO has a total of 31,408,133,379,194,880,000,000 visually distinct positions [https://www.jaapsch.net/puzzles/octaface.htm].

If the X-centers are to be each considered unique, then the number becomes [(6!/2)(2^6/2)(12!/2)(12!/2)^2]/12 = 13,188,400,838,457,446,891,520,000,000 total positions.

== Related Puzzles ==

=== Skewb Diamond ===

{{Main Article|Article=Skewb Diamond}}

[[Image:Skewb_diamond.png|120px]]

The Skewb Diamond, also known as the 2x2 FTO, can be seen as either a face-turning octahedron with deep cuts or a 2-layer version of the standard FTO. It is also an octahedral shape transformation of a [[Skewb]] where the Skewb's centers correspond to the Skewb Diamond's corners and the Skewb's corners correspond to the Skewb Diamond's centers, which means that orientation matters on the opposite pieces as compared to the standard Skewb.

=== Master FTO ===

[[Image:masterfto.png|120px]]

The Master FTO, or 4x4 FTO, is a four-layered face-turning octahedron with two different cut depths (one deep and one shallow) such that the faces appear like those of a [[Master Pyraminx]].

=== Other Related Puzzles ===

There are four distinct face-turning octahedral puzzles that each have a single planar cut depth. From shallowest to deepest, they are the Dino Octahedron, the standard FTO (the main subject of this article), the Master Skewb Diamond, and the Skewb Diamond (discussed above). The Dino Octahedron, briefly produced by MF8, is the shallowest possible face-turning octahedron with one cut per side. It is equivalent to a standard FTO with the addition of fixed centers. The Master Skewb Diamond is a face-turning octahedral puzzle with a cut depth between the standard FTO and the Skewb Diamond, and can be seen as a shape transformation of the Master Skewb. Although it has not yet been mass-produced in its pure form, MF8 has made a "crazy" version with added circular cuts on the faces. The only functional difference between the Dino Octahedron and the Master Skewb Diamond is that the centers are fixed on the Dino Octahedron, whereas they turn with the faces on the Master Skewb Diamond.

== Methods ==

There are many methods used to solve the Face Turning Octahedron, the most popular of which are described below.

=== Bencisco ===

The [[Bencisco method]] is a method based on ending in a step called Last Three Triples and was created by Ben Streeter in 2020.

# First Block: Solve a block on the BL layer consisting of a large hexagon center and two triples. A triple is a corner and two opposite small triangle centers.
# Centers: Solve the remaining three hexagon centers in the layers to the right of the block built in the first step.
# Triple: Rotate to have the upper left corner be at the bottom and solve the unsolved triple at that position.
# Last Three Triples: Middle layer center triangles, last layer center triangles, and last layer corners remain to be solved. Finish the solve by forming three triples then solving them to their correct positions, or solve everything in a single step using 179 algorithms.

=== Nautilus ===

The [[Nautilus (FTO)|Nautilus method]] is an F2L and Last Layer method that was developed by a team consisting of [[James Straughan]], Liam Highducheck, and Vincent Trang, with additional input by Ryan Hudgens and mrmangohands.

# First Block: Solve a block on the BL layer consisting of a large hexagon center and two triples.
# Centers: Solve the remaining three hexagon centers.
# Triple: Solve the last triple at the bottom right, completing the first two layers.
# Last Layer: Solve the last layer. This is typically accomplished by first solving the center triangles then the corners. 1LLL has also been developed.

There are some alternative steps to solving the first two layers that users may prefer:

# First Block: Solve a block on the BL layer consisting of a large hexagon center and two triples.
# Stripe: Solve the F2L stripe to the right of the first block. This leaves just the U and R layers unsolved.
# F2L: Solve the remainder of the F2L using just U and R turns.
# Last Layer: Solve the last layer.

=== Vertigo ===

By Ryan Hudgens and Ben Streeter.

# Vertex: Solve a corner and its surrounding four triangles and four edges.
# Second Vertex: Solve another vertex adjacent to the first. Keep these two at the bottom left of the first two layers.
# Edges and Triangles: Solve the last four edges and the two triangles at either the intersection of DR or UL.
# Last Six Triangles: If in the last step the two triangles at DR were solved, solve the three remaining U face triangles and the three that belong in the middle layer beneath the U layer, equivalent to the E layer on 3x3. Do the opposite of this if in the last step the two triangles at UL were solved.
# Last Three Triples: Finish the solve by forming the last three triples then solving them to their correct positions, or solve everything in a single step using 179 algorithms.

=== CFL ===

CFL is a method similar to CFOP and was created by James Straughan.

# Centers: Solve the three large hexagon centers around the sides of the first two layers.
# F2L: Solve the three triples of the first two layers.
# Last Layer: Solve the last layer. This is typically accomplished by first solving the triangle centers then the corners, but other systems also exist such as OLL then PLL or 1LLL.

Many CFOP techniques can be carried over such as pseudo slotting, edge control (corner control or triangle control in CFL), ZBLS (orienting corners or positioning triangles during the last slot), and XCross (arrow block + centers in CFL).

=== L4T Redux ===

A version of reduction that combines modern techniques with reduction to Pyraminx steps. All of the various Pyraminx steps can be incorporated into the method. The method was developed by Vincent Trang, with some alg development by James Straughan.

# First Block: Solve a block on the BL layer consisting of a large hexagon center and two triples. The two triples can be any triple and not just the ones that belong in those positions. This allows for more freedom in the reduction step.
# Centers: Solve the remaining three hexagon centers.
# Reduction: Form the last four triples using big cube style slicing techniques. This reduces the FTO to a Pyraminx stage.
# Pyra Stage: Solve as a Pyraminx.

=== Julian ===

# Center: Solve a large hexagon center.
# Arrow Blocks: Add two adjacent arrow blocks to the hexagon center.
# Third arrow: Solve the last arrow connected to the hexagon center, but leave out the two triangles that would go around the sides of the layer where the hexagon center is.
# Corners: Solve the last three corners.
# Triangles: Use commutators to solve all remaining small triangle centers.

=== Other F2L Methods ===

Two of the mentioned methods, Nautilus and CFL, involve solving F2L then the last layer. Various 3x3 methods can be adapted to FTO to solve the first two layers [https://sites.google.com/site/athefre/other-puzzles/fto-f2l-methods]. Some of these involve solving F2L from an edge in front perspective, which involves solving a right layer center and left layer block, similar to many big cube methods. This perspective allows for U R r turning that doesn't disturb the built right layer center.

==== LEOR (CIF) ====

# First Block: Solve a block on the BL layer consisting of a large hexagon center and two triples.
# Stripe: Solve the F2L stripe to the right of the first block. This leaves just the U and R layers unsolved.
# F2L: Solve the remainder of the F2L using just U and R turns.
# Last Layer: Solve the last layer.

==== LEOR (EIF) ====

# First Block + Center: Solve the R layer center and a block on the BL layer consisting of a half center and its two outer triangles and a triple on the bottom. This leaves the U layer, R layer triples, and the slice layer between the R and BL layers unsolved.
# Stripe: Solve the F2L stripe between the first block and R layer center.
# F2L: Solve the two remaining F2L triples.
# Last Layer: Solve the last layer.

==== Nautilus (EIF) ====

# First Block + Center: Solve the R layer center and a block on the BL layer consisting of a half center and its two outer triangles and a triple on the bottom. This leaves the U layer, R layer triples, and the slice layer between the R and BL layers unsolved.
# Pyramid: Build a 2x2x2 pyramid on the bottom in the back.
# Stripe: Finish the stripe between the first block and R layer center.
# Last Slot: Solve the last slot, which is the triple on the bottom in the front.
# Last Layer: Solve the last layer.

== Tutorials/Guides ==
* [https://www.youtube.com/watch?v=6JT2tU00ccs Bencisco guide]
* [https://sites.google.com/view/nautilusfto Nautilus website]
* [https://sites.google.com/site/athefre/other-puzzles/cfl?authuser=0 CFL website]
* [https://docs.google.com/document/d/18CMTrFC9PYkEsheOHnywzvV0EdCb3SFGQXSK0DDb30o/edit?pli=1&tab=t.0 L4T Redux guide]
* [https://docs.google.com/spreadsheets/d/1_IHL077w-9U-qtpF9hvC6CrUn7etua5QgPH8vEMqK58/edit?usp=sharing L4T Redux L4E]

[[Category:Twisty puzzles]]

Nautilus (FTO)

2026-08-14T17:58:17Z

Athefre:

{| border="1" class="infobox-template" style="float: right; border-collapse:collapse; width: 22em; font-size: 90%; margin: 0 0 10px 10px;"
|
{| border="0" cellpadding="3" bgcolor="#F0F0F0" cellspacing="2" style="color:black; text-align:center; width: 100%"
|-
| bgcolor="#D0DFEE" colspan="2" style="font-size: 125%;" | '''{{{name|}}} Nautilus (FTO)'''
|-
| colspan="2" style="font-size:90%;"| [[Image:Nautilus(FTO).png|200px]]
|-
| bgcolor="#E0E8EF" colspan="2" | '''Information'''
|-
| bgcolor="#F0F0F0" align="right" | '''Proposer:'''
| align="left" | {{{proposers|[[James Straughan]]}}}
|-
| bgcolor="#F0F0F0" align="right" | '''Developers:'''
| align="left" | {{{proposers|[[James Straughan]], [[Liam Highducheck]], [[Vincent Trang]], [[Malte Ihlefeld]], [[Ryan Hudgens]]}}}
|-
| bgcolor="#F0F0F0" align="right" | '''Proposed:'''
| align="left" | {{{year|2024}}}
|-
| bgcolor="#F0F0F0" align="right" | '''No. Steps:'''
| align="left" | {{{steps|varies}}}
|-
| bgcolor="#F0F0F0" align="right" | '''No. Algs:'''
| align="left" | {{{algs|varies}}}
|-
| bgcolor="#F0F0F0" align="right" | '''Purpose:'''
| align="left" | {{{purpose|[[Speedsolving]]}}}
|-
|}
|}

'''Nautilus''' is an [[Face Turning Octahedron]] speedsolving method developed by James Straughan with assistance from Liam Highducheck and Vincent Trang. The method has a focus on simple, automatic, and algorithm based solving similar to [[CFOP]] for 3x3.

== Steps ==

'''1. First Block:''' Solve the BL layer minus the corner and two small centers of the U layer. More specifically, these pieces are the large center consisting of three edges and three inner centers, the two bottom corners, and the remaining four small center pieces (triangles) around the sides. This step is typically solved by first building the large center. Then two triples (a corner and two attached triangles) are built and attached to the large center.
[[image:NautilusFTOFB.png|300px|center]]
'''2. Centers:''' Solve the F, D, and BR large centers. This will automatically solve the U layer large center.
[[image:NautilusCenters.png|300px|center]]
'''3. Last Triple:''' Complete the F2L by solving the final corner and two triangles. This step can be solved in a single step using algorithms or broken down into two or three steps for more basic solving.
[[image:NautilusLastTriple.png|300px|center]]
'''4. Last Layer:''' Solve the last layer. The standard steps are to solve the side triangles in one step then solve the corners in the second step. Or, 1LLL can be used, which consists of 377 cases. The advantage to ending with a last layer is that recognition is simple. Only the sides of the layer need to be checked to determine a case. There is no need to check the U face or any other pieces around the FTO.
[[image:NautilusLL.png|300px|center]]

== Pros ==

* Simple, automatic steps.
* Algorithm based solving may be faster than intuitive based methods.
* Last layer recognition is simple, requiring only checking the sides of the last layer.

== Cons ==

* Large number of algorithms to learn if learning 1LLL.

== Advancements ==

=== Advanced Last Slot ===

An alternate ending to solving the first two layers is to solve to the F2L-1 equivalent. This leaves a large F2L "pair" that can be solved in a single step. This creates a more advanced two step ending of solving the large pair then 1LLL. The large pair consists of everything except for the right two triangles of the F layer, the edge, the bottom right side triangle, and the corner.

=== Early Corner Orientation ===

The ZBLS equivalent would be to orient the last layer corners during a previous step. This can be accomplished during the last triple step or integrated into the advanced last slot.

=== Four Triples ===

Another possible advancement is to construct four triples at the last triple step. Then solve the four triples. [[Vincent Trang]] developed an intuitive technique for building the triples, but the technique hasn't been perfected. There is also the possibility of building the triples using algorithms, maybe even through integrating a technique similar to [[CLL+1]]. However, the recognition and execution speed hasn't been tested to compare it to the more automated and algorithm based steps currently used.

== Last Layer Variants ==

Other last layer ideas have been proposed:

* Orient the last layer corners then use PLL.
* Solve the three corners then the last six triangles.
* Form the three triples on the last layer in any orientation then solve the triples.
* Orient the last layer corners while solving the last six triangles relative to the corners. This forms three triples that can then be permuted using one of two algorithms. This idea was proposed by Vincent Trang.
* Leave out the bottom right corner and solve all triangles. Then solve the final four corners in a single step.
* Solve one triple in one algorithm then solve the other two corners and four triangles of the last layer in one algorithm.
* Solve two triangles of the last layer then solve the remaining pieces.

== External Links ==
* [https://sites.google.com/view/nautilusfto Official Website]
* [https://discord.gg/GJB2ER2Q3M Discord Server]

[[Category:Acronyms]]

Face Turning Octahedron

2026-08-10T02:29:33Z

Athefre: /* L4T Redux */

{{Puzzle Infobox|
|NAME=Face Turning Octahedron
|IMAGE=Dayan-fto-magnetic-ball-core-stickerless_540x.webp
|ALTERNATIVENAMES=FTO
|MECHANISM=Face Turning Octahedron
|SHAPE=Octahedron
|INVENTOR=David Pitcher
|YEAR=c. 2003
|COMPANIES=[[Dayan]], [[DianSheng]], [[LanLan]], [[Shengshou]], [[Qiyi]], [[Maru]]
|JAAPSCH=octaface}}

The Face Turning Octahedron is a three-layered face turning octahedral puzzle for which all three layers are the same width. The first working version was made by David Pitcher in the early 2000s and was later mass-produced by [[LanLan]]. In 2024, [[DianSheng]] released a magnetic version, which was followed by other speed versions by various companies including [[Dayan]], [[Qiyi]], and [[Shengshou]]. Before these versions were mass-produced, it was common to make one by attaching printed extentions to a Qiyi [[Rex Cube]].

== Basic Characteristics ==
The Face Turning Octahedron is a face-turning regular octahedral puzzle with a cut depth such that the cuts intersect at a point in the center of each face. It is the second shallowest possible planar cut depth of a face-turning octahedral puzzle (with the shallowest being the Dino Octahedron). Its pieces consist of 6 corners, 12 edges, and 24 X-centers. Since rotation about the faces of an octahedron result in two distinct sets of four faces each where a face from one set can never reach the starting position of any face from the other set, the stickers of an FTO are divided into two distinct orbits, where colors of adjacent faces can never end up on the same face. This means that the corners only have two possible orientations per location (when the puzzle is scrambled without cube rotations), the edges are always oriented, and there are two sets of X-centers that never mix. Interestingly, this also means than an FTO stickered with only four colors, with opposite sides having the same color, solves exactly the same way as an FTO stickered with all eight colors.

The corners turn out to be equivalent to pyraminx edges, which means that only even permutations are possible and that a single corner "flip" is impossible. Additionally, since each face turn does a 3-cycle of edges, only even permutations are possible for edges as well.

As calculated by Jaap, the FTO has a total of 31,408,133,379,194,880,000,000 visually distinct positions [https://www.jaapsch.net/puzzles/octaface.htm].

If the X-centers are to be each considered unique, then the number becomes [(6!/2)(2^6/2)(12!/2)(12!/2)^2]/12 = 13,188,400,838,457,446,891,520,000,000 total positions.

== Related Puzzles ==

=== Skewb Diamond ===

{{Main Article|Article=Skewb Diamond}}

[[Image:Skewb_diamond.png|120px]]

The Skewb Diamond, also known as the 2x2 FTO, can be seen as either a face-turning octahedron with deep cuts or a 2-layer version of the standard FTO. It is also an octahedral shape transformation of a [[Skewb]] where the Skewb's centers correspond to the Skewb Diamond's corners and the Skewb's corners correspond to the Skewb Diamond's centers, which means that orientation matters on the opposite pieces as compared to the standard Skewb.

=== Master FTO ===

[[Image:masterfto.png|120px]]

The Master FTO, or 4x4 FTO, is a four-layered face-turning octahedron with two different cut depths (one deep and one shallow) such that the faces appear like those of a [[Master Pyraminx]].

=== Other Related Puzzles ===

There are four distinct face-turning octahedral puzzles that each have a single planar cut depth. From shallowest to deepest, they are the Dino Octahedron, the standard FTO (the main subject of this article), the Master Skewb Diamond, and the Skewb Diamond (discussed above). The Dino Octahedron, briefly produced by MF8, is the shallowest possible face-turning octahedron with one cut per side. It is equivalent to a standard FTO with the addition of fixed centers. The Master Skewb Diamond is a face-turning octahedral puzzle with a cut depth between the standard FTO and the Skewb Diamond, and can be seen as a shape transformation of the Master Skewb. Although it has not yet been mass-produced in its pure form, MF8 has made a "crazy" version with added circular cuts on the faces. The only functional difference between the Dino Octahedron and the Master Skewb Diamond is that the centers are fixed on the Dino Octahedron, whereas they turn with the faces on the Master Skewb Diamond.

== Methods ==

There are many methods used to solve the Face Turning Octahedron, the most popular of which are described below.

=== Bencisco ===

The [[Bencisco method]] was created by Ben Streeter in 2020.

# First Block: Solve a block on the BL layer consisting of a large hexagon center and two triples. A triple is a corner and two opposite small triangle centers.
# Centers: Solve the remaining three hexagon centers in the layers to the right of the block built in the first step.
# Triple: Solve the triple at the upper left on the U layer.
# Last Three Triples: Finish the solve by forming the last three triples then solving them to their correct positions, or solve everything in a single step using 179 algorithms.

=== Nautilus ===

The [[Nautilus (FTO)|Nautilus method]] was developed by a team consisting of [[James Straughan]], Liam Highducheck, and Vincent Trang, with additional input by Ryan Hudgens and mrmangohands.

# First Block: Solve a block on the BL layer consisting of a large hexagon center and two triples.
# Centers: Solve the remaining three hexagon centers.
# Triple: Solve the last triple at the bottom right, completing the first two layers.
# Last Layer: Solve the last layer. This is typically accomplished by first solving the triangle centers then the corners, but other systems also exist such as OLL then PLL, or 1LLL.

There are some alternative steps to solving the first two layers that users may prefer:

# First Block: Solve a block on the BL layer consisting of a large hexagon center and two triples.
# Stripe: Solve the F2L stripe to the right of the first block. This leaves just the U and R layers unsolved.
# F2L: Solve the remainder of the F2L using just U and R turns.
# Last Layer: Solve the last layer.

=== Vertigo ===

By Ryan Hudgens and Ben Streeter.

# Vertex: Solve a corner and its surrounding four triangles and four edges.
# Second Vertex: Solve another vertex adjacent to the first. Keep these two at the bottom left of the first two layers.
# Edges and Triangles: Solve the last four edges and the two triangles at either the intersection of DR or UL.
# Last Six Triangles: If in the last step the two triangles at DR were solved, solve the three remaining U face triangles and the three that belong in the middle layer beneath the U layer, equivalent to the E layer on 3x3. Do the opposite of this if in the last step the two triangles at UL were solved.
# Last Three Triples: Finish the solve by forming the last three triples then solving them to their correct positions, or solve everything in a single step using 179 algorithms.

=== CFL ===

CFL is a method similar to CFOP and was created by James Straughan.

# Centers: Solve the three large hexagon centers around the sides of the first two layers.
# F2L: Solve the three triples of the first two layers.
# Last Layer: Solve the last layer. This is typically accomplished by first solving the triangle centers then the corners, but other systems also exist such as OLL then PLL or 1LLL.

Many CFOP techniques can be carried over such as pseudo slotting, edge control (corner control or triangle control in CFL), ZBLS (orienting corners or positioning triangles during the last slot), and XCross (arrow block + centers in CFL).

=== L4T Redux ===

A version of reduction that combines modern techniques with reduction to Pyraminx steps. All of the various Pyraminx steps can be incorporated into the method. The method was developed by Vincent Trang, with some alg development by James Straughan.

# First Block: Solve a block on the BL layer consisting of a large hexagon center and two triples. The two triples can be any triple and not just the ones that belong in those positions. This allows for more freedom in the reduction step.
# Centers: Solve the remaining three hexagon centers.
# Reduction: Form the last four triples using big cube style slicing techniques. This reduces the FTO to a Pyraminx stage.
# Pyra Stage: Solve as a Pyraminx.

=== Julian ===

# Center: Solve a large hexagon center.
# Arrow Blocks: Add two adjacent arrow blocks to the hexagon center.
# Third arrow: Solve the last arrow connected to the hexagon center, but leave out the two triangles that would go around the sides of the layer where the hexagon center is.
# Corners: Solve the last three corners.
# Triangles: Use commutators to solve all remaining small triangle centers.

== Tutorials/Guides ==
* [https://www.youtube.com/watch?v=6JT2tU00ccs Bencisco guide]
* [https://sites.google.com/view/nautilusfto Nautilus website]
* [https://sites.google.com/site/athefre/other-puzzles/cfl?authuser=0 CFL website]
* [https://docs.google.com/document/d/18CMTrFC9PYkEsheOHnywzvV0EdCb3SFGQXSK0DDb30o/edit?pli=1&tab=t.0 L4T Redux guide]
* [https://docs.google.com/spreadsheets/d/1_IHL077w-9U-qtpF9hvC6CrUn7etua5QgPH8vEMqK58/edit?usp=sharing L4T Redux L4E]

[[Category:Twisty puzzles]]

List of methods

2026-07-21T04:00:58Z

Athefre:

:For a category view, see ''[[:Category:Methods and substeps|Methods and substeps]]''

== Table of methods by purpose ==

The following is a table of methods (and their variants) for solving various twisty puzzles. Follow the links to read more about each method or the methods in the category.

{| class="TablePager" style="padding:3px; border-spacing:0"
!| Name
!| Original Proposer(s)
!| Year
!| Variants
|-
| colspan="4" style="background-color:#d5d5d5; text-align:center;" | '''[[:Category:2x2x2 methods|2x2]]'''
|-
|-
| colspan="4" style="background-color:#f5f5f5; text-align:center;" | '''[[:Category:2x2x2 beginner methods|2x2 Beginner]]'''
|-
| [[LBL]]
|
|
| style="text-align:center;" | Waterman Last Layer
|-
| [http://www.speedsolving.com/wiki/index.php/Beginner_Guimond#Guimond_as_a_Beginner_Method Beginner Guimond]
| [[Conrad Rider]]
|
|-
|-
| colspan="4" style="background-color:#f5f5f5; text-align:center;" | '''[[:Category:2x2x2 speedsolving methods|2x2 Speed]]'''
|-
| [[CLL]]
| Various
|
|-
| [[NMCLL]]
| [[Gilles Roux/old_revision|Gilles Roux]], [http://www.speedsolving.com/wiki/index.php/User:Athefre James Straughan]
|
|-
| [[EG]]
| [[Erik Akkersdijk]], [[Gunnar Krig]]
|
| style="text-align:center;" | EG-1, EG-2
|-
| [[Guimond]]
| [[Gaétan Guimond]]
|
|-
| [[Ortega]]
| [[Victor Ortega]], [[Josef Jelinek]], Jeff Varasano
|
| style="text-align:center;" | PBL
|-
| [[SS]]
| [[Mitchell Stern]], [[Timothy Sun]]
|
|-
| [[OFOTA]]
| [[Erik Akkersdijk]]
|
|-
| [[VOP]]
| [[Kenneth Gustavsson]]
|
|-
| [[GBC]]
| [[Signalcuber]]
|
|-
| [[TCLL]]
| [[Robert Yau]], Christopher Olson, and others
|
| style="text-align:center;" | CLL
|-
| [[HD]]
| V. Higgs, J. Demars, Max Garza, John Lewis
|
| style="text-align:center;" | VOP
|-
| [[BOP]]
| Matthew Pan
|-
| [[MLS]]
| Matthew Pan
|-
| colspan="4" style="background-color:#d5d5d5; text-align:center;" | '''[[:Category:3x3x3 methods|3x3]]'''
|-
|-
| colspan="4" style="background-color:#f5f5f5; text-align:center;" | '''[[:Category:3x3x3 beginner methods|3x3 Beginner]]'''
|-
| [[LBL]]
|
|
|-
| Ortega/Mcetsu
| Jeff Varasano
|
|-
| [[Corners First]]
| [[Marc Waterman]]
|
|-
| [[Less is More]]
| [[Camilo Amaral]]
|
|-
| "[[The Ideal Solution]]"
| Ideal Toy Corp
|
|-
| [[Edges First]]
|
|
|-
| [[8355]]
| [[Reheart Sheu]]
|
| style="text-align:center;" | [[Sexy Method]], [[MirIS Method]]
|-
| [[Edge Supertwist Method]]
| [[David Ha]]
|-
| colspan="4" style="background-color:#f5f5f5; text-align:center;" | '''[[:Category:3x3x3 speedsolving beginner methods|3x3 speed Beginner]]'''
|-
| Beginner CFOP
| Badmephisto
|
|-
| Beginner Roux
|
|
|-
| [[Beginner Petrus]]
|
|
|-
| Pogobat Beginner Method
| Dan Brown
|
|-
| [[Keyhole]]
|
|
|-
| [[XG]]
|
|
| style="text-align:center;" | [[OLL]], [[PLL]]
|-
| [[Samsara Method]]
|
|
| style="text-align:center;" | [[OLL]], [[PLL]]
|-
| [[Lazy CFOP]]
| [[Alex Yang]]
|
| style="text-align:center;" | CFOP, Roux, Petrus, CFCE, ZZ, Columns, LBL, FreeFOP, FreeFCE, WV, Salvia, Snyder
|-
|[[335]]
|[[Robbie Safran]]
|-
|[[CB]]
|[[Allen Milazzo]], [[Joon Johnson]]
|
|-
| colspan="4" style="background-color:#f5f5f5; text-align:center;" | '''[[:Category:3x3x3 speedsolving methods|3x3 Speed]]'''
|-
| [[CFOP]] (Fridrich)
| [[Donald Taylor]], [[John Conway]], [[David Benson]], [[David Seal]], [[Jessica Fridrich]], [[Mirek Goljan]], [[Hans Dockhorn]], [[Anneke Treep]], [[René Schoof]]
| 1979-1981
| style="text-align:center;" | [[VH]], [[ZB]], [[MGLS| MGLS-F]], [[FreeFOP]]
|
|-
| [[CFCE]]
| [[Guus Razoux Schultz]]
| 1981
| style="text-align:center;" |
|
|-
| [[Petrus]]
| [[Lars Petrus]]
| 1981
| style="text-align:center;" |
|
|-
| [[Waterman]]
| [[Marc Waterman]]
| 1981
| style="text-align:center;" |
|
|-
| [[Snyder Method|Snyder Method 2]]
| [[Anthony Snyder]]
| 1982
| style="text-align:center;" |
|
|-
| [[Tripod]]
| [[Ryan Heise]] [[Michael Gottlieb]]
| 2002
| style="text-align:center;" | F2L, 2x2 Block, 2x2x3 Block
|
|-
| [[Doug Li Method|Doug Li]]
| [[Doug Li]]
| 2002
| style="text-align:center;" |
|
|-
| [[Roux]]
| [[Gilles Roux/old_revision|Gilles Roux]]
| 2003
| style="text-align:center;" |
|
|-
| [[Heise]]
| [[Ryan Heise]]
| 2003
| style="text-align:center;" |
|
|-
| [[L2L]]
| [[Duncan Dicks]], [[Stachu Korick]]
| 2004
| style="text-align:center;" |
|
|-
| [[MI1|Solaris]]
| [[James Straughan]]
| 2006
| style="text-align:center;" |
|
|-
| [[Nautilus]]
| [[James Straughan]]
| 2006
| style="text-align:center;" |
|
|-
| [[ZZ]]
| [[Zbigniew Zborowski]]
| 2006
| style="text-align:center;" | [[ZZ-VH]], [[ZZ-a]], [[ZZ-b]], [[ZZ-d]], [[ZZ-WV]], [[MGLS| MGLS-Z]], [[ZZ-blah]], [[EJLS]], [[JTLE]], ZBLL
|
|-
| [[Polaris]]
| [[James Straughan]]
| 2010
| style="text-align:center;" |
|
|-
| [[Hahn]]
| [[Eric Hahn]]
| 2010
| style="text-align:center;" |
|
|-
| [[Pizel method]]
| Alexandre Philiponet
| 2011
| style="text-align:center;" |
|
|-
| [[CEOR]]
| Various
| 2013
| style="text-align:center;" |
|
|-
| [[LEOR]]
| [[Noa Arthurs]]
| 2013
| style="text-align:center;" |
|
|-
| [[SSC]]
| [[Joseph Briggs]]
| 2015
| style="text-align:center;" |
|
|-
| [[M-CELL]]
| [[Joseph Briggs]]
| 2015
| style="text-align:center;" |
|
|-
| [[Hexagonal Francisco]]
| [[Andrew Nathenson]], [[Henry Helmuth]]
| 2016
| style="text-align:center;" |
|
|-
| [[Quadrangular Francisco]]
| [[Alex Yang]]
| 2016
| style="text-align:center;" |
|
|-
| [[2GR]]
| [[John Li]]
| 2017
| style="text-align:center;" |
|
|-
| [[42]]
| [[Joseph Briggs]]
| 2017
| style="text-align:center;" |
|
|-
| [[Zipper]]
| [[Justin Taylor]]
| 2017
| style="text-align:center;" |
|
|-
| [[Ribbon Method|Ribbon]]
| [[Justin Taylor]]
| 2017
| style="text-align:center;" |
|
|-
| [[Sledgehog]]
| [[Ryan Vigil]]
| 2017
| style="text-align:center;" |
|
|-
| [[LMCF]]
| [[Eric Fattah]]
| 2017
| style="text-align:center;" |
|
|-
| [[WaterRoux]]
| [[Eric Fattah]], [[Max Garza]]
| 2017
| style="text-align:center;" |
|
|-
| [[R3T]]
| [[Terence Tan]]
| 2018
| style="text-align:center;" |
|
|-
| [[Tudor]]
| [[Joseph Tudor]]
| 2018
| style="text-align:center;" |
|
|-
| [[Russo]]
| [[Anthony Russo]]
| 2019
| style="text-align:center;" |
|
|-
| [[Square-101]]
| [[Vincent Trang]]
| 2020
| style="text-align:center;" |
|
|-
| [[Mehta]]
| [[Yash Mehta]]
| 2020
| style="text-align:center;" |
|
|-
| [[SSRC]]
| [[Silky]]
| 2020
| style="text-align:center;" |
|
|-
| [[APB]]
| [[James Straughan]]
| 2021
| style="text-align:center;" |
|
|-
| [[Squall]]
| [[Vincent Trang]]
| 2021
| style="text-align:center;" |
|
|-
| [[TruSRU]]
| [[Vincent Trang]]
| 2021
| style="text-align:center;" |
|
|-
| [[Farz]]
| [[Faris Zamani]]
| 2023
| style="text-align:center;" |
|
|-
| [[Peridot]]
| [[Kristopher Tibbetts]]
| 2023
| style="text-align:center;" |
|
|-
| [[Epidote]]
| [[Kristopher Tibbetts]]
| 2023
| style="text-align:center;" |
|
|-
| [[Iacob method|Iacob]]
| [[Iacob Razvan]]
| 2023
| style="text-align:center;" |
|
|-
| [[Hall Method|Hall]]
| [[Daylen Hall]], [[Ethan Hayes]]
| 2023
| style="text-align:center;" |
|
|-
| [[Platform]]
| [[Riccardo Munaro]]
| 2023
| style="text-align:center;" |
|
|-
| [[ECBL]]
| [[Montu]], [[Kristopher Tibbetts]]
| 2024
| style="text-align:center;" |
|
|-
| [[Quipper method|Quipper]]
| [[William Sallros]]
| 2025
| style="text-align:center;" |
|
|-
| [[Petrus-T]]
| [[Gustavo P Leite]], [[Mingus]], [[Major Gilreath]]
| 2025
| style="text-align:center;" |
|
|-
| [[TN]]
| [[Ngô Anh Tuấn]]
| 2025
| style="text-align:center;" |
|
|-
| [[Columns First Methods]]
| Various
| Unknown
| style="text-align:center;" | Roux, CFOP, Shadowslice
|
|-
| colspan="4" style="background-color:#f5f5f5; text-align:center;" | '''[[:Category:3x3x3 speedsolving methods|3x3 Speed]]/[[Fewest Moves techniques|FMC]]'''
|-
| [[Petrus]]
| [[Lars Petrus]]
|
| style="text-align:center;" | [[JTLE]], [[EJLS]], [[MGLS| MGLS-P]]
|-
| [[Heise]]
| [[Ryan Heise]]
|
|-
| [[Mehta]]
| [[Yash Mehta]]
|
|-
| [[Snyder]]
| [[Anthony Snyder]]
|
|-
| [[SSC (Shadowslice Snow Columns)]]
| [[Joseph Briggs]]
|
|-
| [[B2 (Briggs2) Method]] (Briggs/B2)
|
|
|-
| [[LEOR]]
| Arc, Pyjam
|
| style="text-align:center;" | [[EO]], [[ZBLL]]
|-
|
|-
| colspan="4" style="background-color:#f5f5f5; text-align:center;" | '''[[:Category:Blindsolving Methods|3x3 BLD]]'''
|-
| [[3OP]]
| [[John White]]?
|
|-
| [[Old Pochmann]]
| [[Stefan Pochmann]]
|
|-
| [[M2/R2]]
| [[Stefan Pochmann]]
|
| style="text-align:center;" | [[Deadalnix]] ([[M2]]), Freestyle for Dummies ([[R2]])
|-
| [[TuRBo]]
| [[Erik Akkersdijk]]
|
|-
| [[BH]]
| [[Daniel Beyer]], [[Chris Hardwick]]
|
|-
| [[ZBLD]]
| [[Chris Tran]]
|
| style="text-align:center;" | ZBLD-2Cycle, ZBLD-3Cycle
|-
| colspan="4" style="background-color:#f5f5f5; text-align:center;" | '''[[List of 3x3 Domino Subgroup methods|3x3 Domino Subgroup]]'''
|-
| [[N3DR]]
| [[N3RZ]]
|
| style="text-align:center;" | 223, DRL, [[DRPLL]]
|-
| colspan="4" style="background-color:#d5d5d5; text-align:center;" | '''[[:Category:Big Cube Methods|Big Cubes]]'''
|-
| colspan="4" style="background-color:#f5f5f5; text-align:center;" | '''[[:Category:Big Cube Methods|n×n×n / Universal]]'''
|-
| [[Ofapel method]]
| [[Guillaume Erbibou]]
|-
| [[ABCube Method]]
| [[Sandra Workman]]
|-
| colspan="4" style="background-color:#f5f5f5; text-align:center;" | '''[[:Category:Big Cube Methods|Big Cubes Speed]]'''
|-
| [[Yau method]]
| [[Robert Yau]]
|
|-
| [[Hoya method]]
| [[Jong-Ho Jeong]]
|-
| [[4BOP]]
| [[Kristopher Tibbetts]]
|
|-
| [[Obli Method]]
| [[Alex Yang]]
|
|-
| [[Reduction]]
|
|
|-
| [[OBLBL]]
|
|
|-
| [[NS4]]
|
|
|-
| [[4Z4]]
| [[Joseph Tudor]]
|
|-
| [[Cage]]
| [[Per Kristen Fredlund]]
|
|-
| [[Meyer method]]
| [[Richard Meyer]]
|
|-
| [[K4]]
| [[Thom Barlow]]
|
|-
| [[Sandwich]]
| [[Nicholas Ho]]
|
|-
| [[Kenneth's Big Cubes Method]]
| [[Kenneth Gustavsson]]
|
|-
| [[Z4]]
| [[User:Cride5|Conrad Rider]]
|
|-
| [[js4]]
| ??
|
|-
| [[4trus]]
| Owen Smith
|
|-
| [[Lewis Method]]
| John Lewis
|
|-
| [[Pet5]]
| Isabel S.
|
|-
| [[Mehta-MH]]
| Matthew Hinton
|
|-
| [[Mehtad]]
| [[Yash Mehta]]
|
|-
| [[TN4]]
| [[Ngô Anh Tuấn]]
|
|-
| colspan="4" style="background-color:#f5f5f5; text-align:center;" | '''[[:Category:Blindsolving methods|Big Cubes BLD]]'''
|-
|-
| [[r2]]
| [[Erik Akkersdijk]]
|
|-
| [[BH]]
| [[Daniel Beyer]], [[Chris Hardwick]]
|-
| colspan="4" style="background-color:#d5d5d5; text-align:center;" | '''[[:Category:Other puzzles methods|Other puzzles]]'''
|-
|-
| colspan="4" style="background-color:#f5f5f5; text-align:center;" | '''[[:Category:Experimental methods|Experimental]]'''
|-
| [[Human Thistlethwaite]]
| [[Morwen Thistlethwaite]] [[Ryan Heise]]
|
|-
| [[Belt]]
| Various
|
|-
| [[CML-Method]]
| [Various]
|
|-
| [[Salvia Method]]
| [[David Salvia]]
|
|-
| [[Triangular Francisco]]
| [[Michael Gottlieb]]
|
|-
| [[Hexagonal Francisco]]
| [[Andrew Nathenson]], Henry Helmuth
|
|-
| [[Quadrangular Francisco]]
| [[Alex Yang]]
|
|-
| [[Orient First]]
| [[Lars Nielsson]]
|-
| [[F2LL2C]]
| [[Aiad Janis]]
|-
| [[HSC]]
| [[Imam Tanvin Alam]]
|
|-
| [[2GB]]
| [[Imam Tanvin Alam]]
|
|-
| [[E15 / E35]]
| ??
|
|-
| [[Zagorec method]]
| [[Damjan Zagorec]]
|
|-
| [[3CFCEP]]
| ??
|
|-
| [[3CFCE]]
| ??
|
|-
| [[PEG]]
| ??
|
|-
| [[PORT]]
| ??
|
|-
| [[FRED]]
| [[Baian Liu]], [[Timothy Sun]], [[Stachu Korick]]
|
|-
| [[VDW Method]]
| [[Alex VanDerWyst]]
|
| style="text-align:center;" |
|-
| [[Hawaiian Kociemba]]
| [[Michael Humuhumunukunukuapua'a]]
|
| style="text-align:center;" | HKOLL, HKPLL, EO,
|-
| [[Pikas**t]]
| Justin Harder
|
|-
| [[Poux]]
| [[Alex Yang]]
|
|-
| [[Roux-CFOP hybrid]]
| Tao Yu (and probably others)
|
|-
| [[1/162]]
| Emil Zedelius
|
|-
|-
| colspan="4" style="background-color:#f5f5f5; text-align:center;" | '''[[Pyraminx methods|Pyraminx]]'''
|-
| [[Pyraminx methods|Corners First]]
| ??
|
|-
| [[Pyraminx methods|Layer First]]
| ??
|
|-
| [[Pyraminx methods|Last 4 Edges]]
| ??
|
|-
| [[Pyraminx methods|Petrus]]
| ??
|
|-
| [[Pyraminx methods|Face Permute]]
| ??
|
|-
| [[Pyraminx methods|WO]]
| [[Oscar Roth Andersen]] (Odder)
|
|-
| [[Pyraminx methods|Oka Method]]
| [[Yohei Oka]]
|
|-
| colspan="4" style="background-color:#f5f5f5; text-align:center;" | '''[[Megaminx methods|Megaminx]]'''
|-
| [[Balint method]]
| Balint Bodor
|
|-
| keyhole method
|
|
|-
|[[S2L Westlund Style]]
|Simon Westlund
|
|-
|S2L+T2L--->Multiple F2L (Virus S2L)
| [[Yu Da Hyun]]
|
|-
| colspan="4" style="background-color:#f5f5f5; text-align:center;" | '''[[Square-1 methods|Square-1]]'''
|-
| [[SSS1M]]
| [[Shelley Chang]]
|
|-
| [[Vandenbergh Method]]
| [[Lars Vandenbergh]]
|
| style="text-align:center;" | EO, CP, EP
|-
| [[Roux n Skrew]]
|
|
|-
| LBL
|
|
| style="text-align:center;" | PLL
|-
| [[Skwuction]]
| Jaap Scherphuis, Cary Huang
|
|-
| [[Yoyleberry]]
| Cary Huang
|
|-
| [[Lin]]
| [[Tse-Kan Lin]]
|
|-
| [[JQ]]
| Jack Triton
|
|-
| colspan="4" style="background-color:#f5f5f5; text-align:center;" | '''[[List of Rubik's Clock methods|Rubik's Clock]]'''
|-
| ...
|
|
|-
| colspan="4" style="background-color:#f5f5f5; text-align:center;" | '''[[List of Rubik's Magic methods|Magic]]'''
|-
| ...
|
|
|-
| colspan="4" style="background-color:#f5f5f5; text-align:center;" | '''[[List of Master Magic methods|Master Magic]]'''
|-
| [[Pochmann Method]]
| [[Stefan Pochmann]]
|
|-
| [[Ooms]]
| [[Alexander Ooms]]
|
|-
| colspan="4" style="background-color:#f5f5f5; text-align:center;" | '''[[List of Skewb methods|Skewb]]'''
|-
| Sarah method
| Sarah Strong
|
| style="text-align:center;" | LBL, 1LLL
|-
| Ranzha method
| Brandon Harnish
|
| style="text-align:center;" | Petrus Block, Welder mask, PUC (Permuting U corners), LFC(Last Four Centers), CLL
|-
| Frisk Method
| [[Alex Yang]]
|
| style="text-align:center;" | VHLS, EG-2
|-
| Skrouxb
| Ben Pang
|
|-
| 1 Algorithm method
| ??
|
| style="text-align:center;" | FBF (Face by Face), CLL
|-
| Kirjava-Meep Method
| Kirjava-Meep
|
| style="text-align:center;" | CLL, EG, L5C, TCLL
|-
| colspan="4" style="background-color:#f5f5f5; text-align:center;" | '''[[List of Rubik's 360 methods|Rubik's 360]]'''
|
|-
| ...
|}

== See also ==
* [[Substep]]
* [[:Category:Substeps|Common substeps]]
* [[Algorithm Database]]
* [[List of Subsets]]
* [[Solving Variants]]

== External links ==
* Speedsolving.com: [http://www.speedsolving.com/forum/showthread.php?t=2402 BCE Methods] - methods based around Blockbuilding, Corners First and Edges First.

[[Category:Lists|methods]]

List of methods

2026-07-20T21:33:38Z

Athefre:

:For a category view, see ''[[:Category:Methods and substeps|Methods and substeps]]''

== Table of methods by purpose ==

The following is a table of methods (and their variants) for solving various twisty puzzles. Follow the links to read more about each method or the methods in the category.

{| class="TablePager" style="padding:3px; border-spacing:0"
!| Name
!| Original Proposer(s)
!| Year
!| Variants
|-
| colspan="4" style="background-color:#d5d5d5; text-align:center;" | '''[[:Category:2x2x2 methods|2x2]]'''
|-
|-
| colspan="4" style="background-color:#f5f5f5; text-align:center;" | '''[[:Category:2x2x2 beginner methods|2x2 Beginner]]'''
|-
| [[LBL]]
|
|
| style="text-align:center;" | Waterman Last Layer
|-
| [http://www.speedsolving.com/wiki/index.php/Beginner_Guimond#Guimond_as_a_Beginner_Method Beginner Guimond]
| [[Conrad Rider]]
|
|-
|-
| colspan="4" style="background-color:#f5f5f5; text-align:center;" | '''[[:Category:2x2x2 speedsolving methods|2x2 Speed]]'''
|-
| [[CLL]]
| Various
|
|-
| [[NMCLL]]
| [[Gilles Roux/old_revision|Gilles Roux]], [http://www.speedsolving.com/wiki/index.php/User:Athefre James Straughan]
|
|-
| [[EG]]
| [[Erik Akkersdijk]], [[Gunnar Krig]]
|
| style="text-align:center;" | EG-1, EG-2
|-
| [[Guimond]]
| [[Gaétan Guimond]]
|
|-
| [[Ortega]]
| [[Victor Ortega]], [[Josef Jelinek]], Jeff Varasano
|
| style="text-align:center;" | PBL
|-
| [[SS]]
| [[Mitchell Stern]], [[Timothy Sun]]
|
|-
| [[OFOTA]]
| [[Erik Akkersdijk]]
|
|-
| [[VOP]]
| [[Kenneth Gustavsson]]
|
|-
| [[GBC]]
| [[Signalcuber]]
|
|-
| [[TCLL]]
| [[Robert Yau]], Christopher Olson, and others
|
| style="text-align:center;" | CLL
|-
| [[HD]]
| V. Higgs, J. Demars, Max Garza, John Lewis
|
| style="text-align:center;" | VOP
|-
| [[BOP]]
| Matthew Pan
|-
| [[MLS]]
| Matthew Pan
|-
| colspan="4" style="background-color:#d5d5d5; text-align:center;" | '''[[:Category:3x3x3 methods|3x3]]'''
|-
|-
| colspan="4" style="background-color:#f5f5f5; text-align:center;" | '''[[:Category:3x3x3 beginner methods|3x3 Beginner]]'''
|-
| [[LBL]]
|
|
|-
| Ortega/Mcetsu
| Jeff Varasano
|
|-
| [[Corners First]]
| [[Marc Waterman]]
|
|-
| [[Less is More]]
| [[Camilo Amaral]]
|
|-
| "[[The Ideal Solution]]"
| Ideal Toy Corp
|
|-
| [[Edges First]]
|
|
|-
| [[8355]]
| [[Reheart Sheu]]
|
| style="text-align:center;" | [[Sexy Method]], [[MirIS Method]]
|-
| [[Edge Supertwist Method]]
| [[David Ha]]
|-
| colspan="4" style="background-color:#f5f5f5; text-align:center;" | '''[[:Category:3x3x3 speedsolving beginner methods|3x3 speed Beginner]]'''
|-
| Beginner CFOP
| Badmephisto
|
|-
| Beginner Roux
|
|
|-
| [[Beginner Petrus]]
|
|
|-
| Pogobat Beginner Method
| Dan Brown
|
|-
| [[Keyhole]]
|
|
|-
| [[XG]]
|
|
| style="text-align:center;" | [[OLL]], [[PLL]]
|-
| [[Samsara Method]]
|
|
| style="text-align:center;" | [[OLL]], [[PLL]]
|-
| [[Lazy CFOP]]
| [[Alex Yang]]
|
| style="text-align:center;" | CFOP, Roux, Petrus, CFCE, ZZ, Columns, LBL, FreeFOP, FreeFCE, WV, Salvia, Snyder
|-
|[[335]]
|[[Robbie Safran]]
|-
|[[CB]]
|[[Allen Milazzo]], [[Joon Johnson]]
|
|-
| colspan="4" style="background-color:#f5f5f5; text-align:center;" | '''[[:Category:3x3x3 speedsolving methods|3x3 Speed]]'''
|-
| [[CFOP]] (Fridrich)
| [[Donald Taylor]], [[John Conway]], [[David Benson]], [[David Seal]], [[Jessica Fridrich]], [[Mirek Goljan]], [[Hans Dockhorn]], [[Anneke Treep]], [[René Schoof]]
| 1979-1981
| style="text-align:center;" | [[VH]], [[ZB]], [[MGLS| MGLS-F]], [[FreeFOP]]
|
|-
| [[CFCE]]
| [[Guus Razoux Schultz]]
| 1981
| style="text-align:center;" |
|
|-
| [[Petrus]]
| [[Lars Petrus]]
| 1981
| style="text-align:center;" |
|
|-
| [[Waterman]]
| [[Marc Waterman]]
| 1981
| style="text-align:center;" |
|
|-
| [[Snyder Method|Snyder Method 2]]
| [[Anthony Snyder]]
| 1982
| style="text-align:center;" |
|
|-
| [[Tripod]]
| [[Ryan Heise]] [[Michael Gottlieb]]
| 2002
| style="text-align:center;" | F2L, 2x2 Block, 2x2x3 Block
|
|-
| [[Doug Li Method|Doug Li]]
| [[Doug Li]]
| 2002
| style="text-align:center;" |
|
|-
| [[Roux]]
| [[Gilles Roux/old_revision|Gilles Roux]]
| 2003
| style="text-align:center;" |
|
|-
| [[Heise]]
| [[Ryan Heise]]
| 2003
| style="text-align:center;" |
|
|-
| [[L2L]]
| [[Duncan Dicks]], [[Stachu Korick]]
| 2004
| style="text-align:center;" |
|
|-
| [[MI1|Solaris]]
| [[James Straughan]]
| 2010
| style="text-align:center;" |
|
|-
| [[Nautilus]]
| [[James Straughan]]
| 2006
| style="text-align:center;" |
|
|-
| [[ZZ]]
| [[Zbigniew Zborowski]]
| 2006
| style="text-align:center;" | [[ZZ-VH]], [[ZZ-a]], [[ZZ-b]], [[ZZ-d]], [[ZZ-WV]], [[MGLS| MGLS-Z]], [[ZZ-blah]], [[EJLS]], [[JTLE]], ZBLL
|
|-
| [[Polaris]]
| [[James Straughan]]
| 2010
| style="text-align:center;" |
|
|-
| [[Hahn]]
| [[Eric Hahn]]
| 2010
| style="text-align:center;" |
|
|-
| [[Pizel method]]
| Alexandre Philiponet
| 2011
| style="text-align:center;" |
|
|-
| [[CEOR]]
| Various
| 2013
| style="text-align:center;" |
|
|-
| [[LEOR]]
| [[Noa Arthurs]]
| 2013
| style="text-align:center;" |
|
|-
| [[SSC]]
| [[Joseph Briggs]]
| 2015
| style="text-align:center;" |
|
|-
| [[M-CELL]]
| [[Joseph Briggs]]
| 2015
| style="text-align:center;" |
|
|-
| [[Hexagonal Francisco]]
| [[Andrew Nathenson]], [[Henry Helmuth]]
| 2016
| style="text-align:center;" |
|
|-
| [[Quadrangular Francisco]]
| [[Alex Yang]]
| 2016
| style="text-align:center;" |
|
|-
| [[2GR]]
| [[John Li]]
| 2017
| style="text-align:center;" |
|
|-
| [[42]]
| [[Joseph Briggs]]
| 2017
| style="text-align:center;" |
|
|-
| [[Zipper]]
| [[Justin Taylor]]
| 2017
| style="text-align:center;" |
|
|-
| [[Ribbon Method|Ribbon]]
| [[Justin Taylor]]
| 2017
| style="text-align:center;" |
|
|-
| [[Sledgehog]]
| [[Ryan Vigil]]
| 2017
| style="text-align:center;" |
|
|-
| [[LMCF]]
| [[Eric Fattah]]
| 2017
| style="text-align:center;" |
|
|-
| [[WaterRoux]]
| [[Eric Fattah]], [[Max Garza]]
| 2017
| style="text-align:center;" |
|
|-
| [[R3T]]
| [[Terence Tan]]
| 2018
| style="text-align:center;" |
|
|-
| [[Tudor]]
| [[Joseph Tudor]]
| 2018
| style="text-align:center;" |
|
|-
| [[Russo]]
| [[Anthony Russo]]
| 2019
| style="text-align:center;" |
|
|-
| [[Square-101]]
| [[Vincent Trang]]
| 2020
| style="text-align:center;" |
|
|-
| [[Mehta]]
| [[Yash Mehta]]
| 2020
| style="text-align:center;" |
|
|-
| [[SSRC]]
| [[Silky]]
| 2020
| style="text-align:center;" |
|
|-
| [[APB]]
| [[James Straughan]]
| 2021
| style="text-align:center;" |
|
|-
| [[Squall]]
| [[Vincent Trang]]
| 2021
| style="text-align:center;" |
|
|-
| [[TruSRU]]
| [[Vincent Trang]]
| 2021
| style="text-align:center;" |
|
|-
| [[Farz]]
| [[Faris Zamani]]
| 2023
| style="text-align:center;" |
|
|-
| [[Peridot]]
| [[Kristopher Tibbetts]]
| 2023
| style="text-align:center;" |
|
|-
| [[Epidote]]
| [[Kristopher Tibbetts]]
| 2023
| style="text-align:center;" |
|
|-
| [[Iacob method|Iacob]]
| [[Iacob Razvan]]
| 2023
| style="text-align:center;" |
|
|-
| [[Hall Method|Hall]]
| [[Daylen Hall]], [[Ethan Hayes]]
| 2023
| style="text-align:center;" |
|
|-
| [[Platform]]
| [[Riccardo Munaro]]
| 2023
| style="text-align:center;" |
|
|-
| [[ECBL]]
| [[Montu]], [[Kristopher Tibbetts]]
| 2024
| style="text-align:center;" |
|
|-
| [[Quipper method|Quipper]]
| [[William Sallros]]
| 2025
| style="text-align:center;" |
|
|-
| [[Petrus-T]]
| [[Gustavo P Leite]], [[Mingus]], [[Major Gilreath]]
| 2025
| style="text-align:center;" |
|
|-
| [[TN]]
| [[Ngô Anh Tuấn]]
| 2025
| style="text-align:center;" |
|
|-
| [[Columns First Methods]]
| Various
| Unknown
| style="text-align:center;" | Roux, CFOP, Shadowslice
|
|-
| colspan="4" style="background-color:#f5f5f5; text-align:center;" | '''[[:Category:3x3x3 speedsolving methods|3x3 Speed]]/[[Fewest Moves techniques|FMC]]'''
|-
| [[Petrus]]
| [[Lars Petrus]]
|
| style="text-align:center;" | [[JTLE]], [[EJLS]], [[MGLS| MGLS-P]]
|-
| [[Heise]]
| [[Ryan Heise]]
|
|-
| [[Mehta]]
| [[Yash Mehta]]
|
|-
| [[Snyder]]
| [[Anthony Snyder]]
|
|-
| [[SSC (Shadowslice Snow Columns)]]
| [[Joseph Briggs]]
|
|-
| [[B2 (Briggs2) Method]] (Briggs/B2)
|
|
|-
| [[LEOR]]
| Arc, Pyjam
|
| style="text-align:center;" | [[EO]], [[ZBLL]]
|-
|
|-
| colspan="4" style="background-color:#f5f5f5; text-align:center;" | '''[[:Category:Blindsolving Methods|3x3 BLD]]'''
|-
| [[3OP]]
| [[John White]]?
|
|-
| [[Old Pochmann]]
| [[Stefan Pochmann]]
|
|-
| [[M2/R2]]
| [[Stefan Pochmann]]
|
| style="text-align:center;" | [[Deadalnix]] ([[M2]]), Freestyle for Dummies ([[R2]])
|-
| [[TuRBo]]
| [[Erik Akkersdijk]]
|
|-
| [[BH]]
| [[Daniel Beyer]], [[Chris Hardwick]]
|
|-
| [[ZBLD]]
| [[Chris Tran]]
|
| style="text-align:center;" | ZBLD-2Cycle, ZBLD-3Cycle
|-
| colspan="4" style="background-color:#f5f5f5; text-align:center;" | '''[[List of 3x3 Domino Subgroup methods|3x3 Domino Subgroup]]'''
|-
| [[N3DR]]
| [[N3RZ]]
|
| style="text-align:center;" | 223, DRL, [[DRPLL]]
|-
| colspan="4" style="background-color:#d5d5d5; text-align:center;" | '''[[:Category:Big Cube Methods|Big Cubes]]'''
|-
| colspan="4" style="background-color:#f5f5f5; text-align:center;" | '''[[:Category:Big Cube Methods|n×n×n / Universal]]'''
|-
| [[Ofapel method]]
| [[Guillaume Erbibou]]
|-
| [[ABCube Method]]
| [[Sandra Workman]]
|-
| colspan="4" style="background-color:#f5f5f5; text-align:center;" | '''[[:Category:Big Cube Methods|Big Cubes Speed]]'''
|-
| [[Yau method]]
| [[Robert Yau]]
|
|-
| [[Hoya method]]
| [[Jong-Ho Jeong]]
|-
| [[4BOP]]
| [[Kristopher Tibbetts]]
|
|-
| [[Obli Method]]
| [[Alex Yang]]
|
|-
| [[Reduction]]
|
|
|-
| [[OBLBL]]
|
|
|-
| [[NS4]]
|
|
|-
| [[4Z4]]
| [[Joseph Tudor]]
|
|-
| [[Cage]]
| [[Per Kristen Fredlund]]
|
|-
| [[Meyer method]]
| [[Richard Meyer]]
|
|-
| [[K4]]
| [[Thom Barlow]]
|
|-
| [[Sandwich]]
| [[Nicholas Ho]]
|
|-
| [[Kenneth's Big Cubes Method]]
| [[Kenneth Gustavsson]]
|
|-
| [[Z4]]
| [[User:Cride5|Conrad Rider]]
|
|-
| [[js4]]
| ??
|
|-
| [[4trus]]
| Owen Smith
|
|-
| [[Lewis Method]]
| John Lewis
|
|-
| [[Pet5]]
| Isabel S.
|
|-
| [[Mehta-MH]]
| Matthew Hinton
|
|-
| [[Mehtad]]
| [[Yash Mehta]]
|
|-
| [[TN4]]
| [[Ngô Anh Tuấn]]
|
|-
| colspan="4" style="background-color:#f5f5f5; text-align:center;" | '''[[:Category:Blindsolving methods|Big Cubes BLD]]'''
|-
|-
| [[r2]]
| [[Erik Akkersdijk]]
|
|-
| [[BH]]
| [[Daniel Beyer]], [[Chris Hardwick]]
|-
| colspan="4" style="background-color:#d5d5d5; text-align:center;" | '''[[:Category:Other puzzles methods|Other puzzles]]'''
|-
|-
| colspan="4" style="background-color:#f5f5f5; text-align:center;" | '''[[:Category:Experimental methods|Experimental]]'''
|-
| [[Human Thistlethwaite]]
| [[Morwen Thistlethwaite]] [[Ryan Heise]]
|
|-
| [[Belt]]
| Various
|
|-
| [[CML-Method]]
| [Various]
|
|-
| [[Salvia Method]]
| [[David Salvia]]
|
|-
| [[Triangular Francisco]]
| [[Michael Gottlieb]]
|
|-
| [[Hexagonal Francisco]]
| [[Andrew Nathenson]], Henry Helmuth
|
|-
| [[Quadrangular Francisco]]
| [[Alex Yang]]
|
|-
| [[Orient First]]
| [[Lars Nielsson]]
|-
| [[F2LL2C]]
| [[Aiad Janis]]
|-
| [[HSC]]
| [[Imam Tanvin Alam]]
|
|-
| [[2GB]]
| [[Imam Tanvin Alam]]
|
|-
| [[E15 / E35]]
| ??
|
|-
| [[Zagorec method]]
| [[Damjan Zagorec]]
|
|-
| [[3CFCEP]]
| ??
|
|-
| [[3CFCE]]
| ??
|
|-
| [[PEG]]
| ??
|
|-
| [[PORT]]
| ??
|
|-
| [[FRED]]
| [[Baian Liu]], [[Timothy Sun]], [[Stachu Korick]]
|
|-
| [[VDW Method]]
| [[Alex VanDerWyst]]
|
| style="text-align:center;" |
|-
| [[Hawaiian Kociemba]]
| [[Michael Humuhumunukunukuapua'a]]
|
| style="text-align:center;" | HKOLL, HKPLL, EO,
|-
| [[Pikas**t]]
| Justin Harder
|
|-
| [[Poux]]
| [[Alex Yang]]
|
|-
| [[Roux-CFOP hybrid]]
| Tao Yu (and probably others)
|
|-
| [[1/162]]
| Emil Zedelius
|
|-
|-
| colspan="4" style="background-color:#f5f5f5; text-align:center;" | '''[[Pyraminx methods|Pyraminx]]'''
|-
| [[Pyraminx methods|Corners First]]
| ??
|
|-
| [[Pyraminx methods|Layer First]]
| ??
|
|-
| [[Pyraminx methods|Last 4 Edges]]
| ??
|
|-
| [[Pyraminx methods|Petrus]]
| ??
|
|-
| [[Pyraminx methods|Face Permute]]
| ??
|
|-
| [[Pyraminx methods|WO]]
| [[Oscar Roth Andersen]] (Odder)
|
|-
| [[Pyraminx methods|Oka Method]]
| [[Yohei Oka]]
|
|-
| colspan="4" style="background-color:#f5f5f5; text-align:center;" | '''[[Megaminx methods|Megaminx]]'''
|-
| [[Balint method]]
| Balint Bodor
|
|-
| keyhole method
|
|
|-
|[[S2L Westlund Style]]
|Simon Westlund
|
|-
|S2L+T2L--->Multiple F2L (Virus S2L)
| [[Yu Da Hyun]]
|
|-
| colspan="4" style="background-color:#f5f5f5; text-align:center;" | '''[[Square-1 methods|Square-1]]'''
|-
| [[SSS1M]]
| [[Shelley Chang]]
|
|-
| [[Vandenbergh Method]]
| [[Lars Vandenbergh]]
|
| style="text-align:center;" | EO, CP, EP
|-
| [[Roux n Skrew]]
|
|
|-
| LBL
|
|
| style="text-align:center;" | PLL
|-
| [[Skwuction]]
| Jaap Scherphuis, Cary Huang
|
|-
| [[Yoyleberry]]
| Cary Huang
|
|-
| [[Lin]]
| [[Tse-Kan Lin]]
|
|-
| [[JQ]]
| Jack Triton
|
|-
| colspan="4" style="background-color:#f5f5f5; text-align:center;" | '''[[List of Rubik's Clock methods|Rubik's Clock]]'''
|-
| ...
|
|
|-
| colspan="4" style="background-color:#f5f5f5; text-align:center;" | '''[[List of Rubik's Magic methods|Magic]]'''
|-
| ...
|
|
|-
| colspan="4" style="background-color:#f5f5f5; text-align:center;" | '''[[List of Master Magic methods|Master Magic]]'''
|-
| [[Pochmann Method]]
| [[Stefan Pochmann]]
|
|-
| [[Ooms]]
| [[Alexander Ooms]]
|
|-
| colspan="4" style="background-color:#f5f5f5; text-align:center;" | '''[[List of Skewb methods|Skewb]]'''
|-
| Sarah method
| Sarah Strong
|
| style="text-align:center;" | LBL, 1LLL
|-
| Ranzha method
| Brandon Harnish
|
| style="text-align:center;" | Petrus Block, Welder mask, PUC (Permuting U corners), LFC(Last Four Centers), CLL
|-
| Frisk Method
| [[Alex Yang]]
|
| style="text-align:center;" | VHLS, EG-2
|-
| Skrouxb
| Ben Pang
|
|-
| 1 Algorithm method
| ??
|
| style="text-align:center;" | FBF (Face by Face), CLL
|-
| Kirjava-Meep Method
| Kirjava-Meep
|
| style="text-align:center;" | CLL, EG, L5C, TCLL
|-
| colspan="4" style="background-color:#f5f5f5; text-align:center;" | '''[[List of Rubik's 360 methods|Rubik's 360]]'''
|
|-
| ...
|}

== See also ==
* [[Substep]]
* [[:Category:Substeps|Common substeps]]
* [[Algorithm Database]]
* [[List of Subsets]]
* [[Solving Variants]]

== External links ==
* Speedsolving.com: [http://www.speedsolving.com/forum/showthread.php?t=2402 BCE Methods] - methods based around Blockbuilding, Corners First and Edges First.

[[Category:Lists|methods]]

ZBLL

2026-07-13T02:18:27Z

Athefre:

{{Substep Infobox
|name=ZBLL
|image=ZBLL.png
|proposers=[[Lars Petrus]], Bernard Helmstetter
|year=2002
|anames=[[ZZ-a]], Steps 5+6+7 ([[Petrus method]])
|variants=[[1LLL]]
|subgroup=[[1LLL]]
|algs=493
|moves=12.08 (Optimal [[HTM]])
|purpose=
* [[Speedsolving]], [[FMC]]
|previous=[[LL:EO cube state]]
|next=[[Solved cube state]]
}}

'''ZBLL''' is a step in many methods which involves solving the entire [[last layer]] in one step, assuming that the [[edge]]s are already oriented. This is part of the [[ZB method]], but it can be useful for any other method which leaves the edges of the last layer oriented after F2L is solved (such as the [[Petrus method]], or [[ZZ Method]]). According to Zborowski's [https://web.archive.org/web/20031004211939/http://www.zborowski.republika.pl/expert3x3x3methodstep3.html webpage], Bernard Helmstetter created the original algorithms for [[Lars Petrus]], who proposed solving the last layer in one step. For this reason, [https://www.speedsolving.com/threads/zbll-history-and-making-the-case-for-a-name-change-phll-hpll.86829/ some in the community] prefer calling this subset PHLL or HPLL and believe that the acronym ZBLL (short for ''[[Zbigniew Zborowski|Zborowski]]-[[Ron van Bruchem|Bruchem]] Last Layer'') does not give proper credit to the original proposers.

ZBLL indeed sounds like a very useful step to learn, but the main reason that it is not in wide use is that it involves a massive total of 493 cases (including PLL). Only a handful of people have ever learned this step in its entirety. If you wish to learn it, it is useful to start by learning either [[OCLL]]/[[PLL]] or [[COLL]]/[[EPLL]] before you learn ZBLL, so that you will always be able to finish the cube relatively quickly even if you do not yet know the ZBLL case. Past that, the learning process is done however you'd like to do it. Many choose to skip learning the S and AS subsets due to their already very easy OLL cases. However, you will benefit if you also learn S and AS.

==Learning Approach==

The ZBLL cases are divided into 8 sets: T, U, L, Pi, Sune, Anti-sune, H, and the PLL (or O) cases, in which all pieces are oriented. The sets are then divided further into 6 subsets. They are recognized by their [[COLL]] case as well as a corresponding edge cycle. Every subset contains 12 cases, which are all different edge cycles possible with the COLL case of that set. Many people recognize ZBLL by looking at the UFR corner and its neighboring stickers. Whether the stickers are adjacent, or opposite allows for a quick recognition. Another way to recognize is through blocks of colour or simply the edge cycle.

==Edge recognition==

For the T, U and L cases (there are 3*6*12=216 algorithms in this set) recognition goes as follows:

1. Recognize the orientation case.

2. Recognize the [[COLL]] case.

3. Recognize the edge cycle by looking at the UFR corner and the edge stickers around it.

4. Apply the corresponding algorithm.

Step 3 may look a little complicated, but it's actually not too bad. In total there are 12 cases, but those are recognized by 2 minor sub-cases, of which there are 3:

C: If the FU sticker is the same as the FRU sticker, and if the RU sticker is the same as the RUF sticker.

A: If the FU sticker is an adjacent color to the FRU sticker, and if the RU sticker is an adjacent color to the RUF sticker.

O: If FU and FRU are opposite, and if RU and RUF are opposite.

A case is recognized by the combination of those. First comes the FU/FRU relation, then the RU/RUF relation, divided by a slash. That means there are 9 possibilities with these cases: C/C, C/A, C/O, A/C, A/A, A/O, O/C, O/A, O/O. However, there are 12 cases. That's because the A case can mean 2 stickers. That's why the last 3 cases are known as C/OX, O/CX and OppX. This means that you don't look for the relation between FU/FRU and RU/RUF, but between FU/RUF and RU/FRU. In the C/OX case, FU and RUF are the same, and RU and FRU are opposite to each other. The same goes for the O/CX case, but vice versa. In the OppX case, both FU/RUF and RU/FRU are opposite. This looks like a Z-permutation. Note that all of these cases can be seen as A/A cases at first, but whenever you have an A/A case, you should always look if it isn't the other one.

== Pros ==
* Smaller movecount than doing OLL/PLL
* Faster than doing OLL/PLL because you only need 1 look

== Cons ==
* There are a total of 493 algorithms
* Long and hard recognition
* Requires edge orientation before doing ZBLL
* Only shows up 1 in 8 solves, however you can make it show up more often by learning ZBLS

== Recognition Methods ==

Various recognition methods have been developed for the step.

=== BH ===

First determine the orientation of the U face corner stickers. Then check pre-determined corner locations for a pattern and compare this with the edges currently around the corner at UFR (the UF and UR edges). The U layer may need to be adjusted if patterns haven’t been learned for all four angles of each case. BH was created by [[Dan Harris]] and [[Jason Baum]].

[[image:BH.png|300px|center]]

=== Blocks ===

Working sort of like 2 sided PLL recognition, patterns of groups of stickers are checked. Adjacent or matching pairs of stickers, a 1x2x2 block, and other patterns.

[[image:ZBLL-Blocks.png|300px|center]]

=== Twisty PLL ===

Like two sided PLL recognition the five pieces within the UF and UR bars are used to determine the case. The corners are mentally twisted, with deduction occasionally involved, to picture the six sticker two sided PLL recognition case. This PLL case, combined with the corner orientation, reveals the case.

[[image:TwistyPLL.png|300px|center]]

=== Tran ===

Similar to BH, the COLL case is first identified. Then locate the two edges that belong around the UFR corner of the chosen U layer angle, rather than the edges currently in those positions. This recognition system was suggested by [[Chris Tran]].

[[image:ZBLL-Tran.png|300px|center]]

=== Tran V2 ===

The original Tran recognition chooses a corner among the seven non-PLL orientations to be considered the UFR corner for locating specific edges. An issue is that if that UFR corner is at UFL, ULB, or UBR and one or both non U face stickers aren’t visible, deduction has to be used in order to know the exact corner and to be able to proceed with locating the edges that belong around it. Tran V2 solves this problem by assigning a corner reference sticker to each U orientation set that is always on the U face, and the edges to be found are changed to become the one matching the corner reference sticker and the one opposite to it. [[Ryan Hudgens]] developed the Tran V2 system.

[[image:ZBLL-TranV2.png|300px|center]]

=== NCP (No CP) ===

After checking the U sticker orientation, the corner permutation pattern is ignored. Instead, look at the 1x2x2 around the UFL corner and the 1x2x2 around the UFR corner. These two patterns narrow down the exact case. This recognition system was developed by Ryan Hudgens.

[[image:NCP.png|300px|center]]

=== Straughan (positional) ===

Only the visible stickers within UFL, the UF edge, UFR, the UR edge, and UBR are checked. The UBL corner and the LUF and BRU stickers aren't used. This combines the pattern based recognition of BH with Twisty PLL's checking of fewer pieces. The result is fewer pieces and fewer stickers, and no deduction or mental corner twisting. It is a requirement to learn the four angles per case, meaning more learning effort from the beginning, but being fully multi-angle from the start. The differences between positional Straughan recognition and Twisty PLL are that the positional Straughan recognition doesn’t involve reducing to PLL recognition and there is no mental corner twisting or deduction. This recognition method was developed by [[James Straughan | Michael James Straughan]].

[[image:ZBLL-Straughan-Positional.png|300px|center]]

=== Straughan (object) ===

The minimum number of stickers necessary to determine any ZBLL case is six. The primary form of this recognition involves locating the six stickers that belong at FLU, FU, FUR, RFU, RU, and RUB. Those six stickers are enough to narrow down the exact case. The stickers that belong oriented to the U face aren't checked. The intended use is for prediction during the solve or for one-looking during inspection, and not for recognition upon arriving at the step. This recognition method was developed by [[James Straughan | Michael James Straughan]].

[[image:ZBLL-Straughan-Object.png|150px|center]]

=== Polar ===

This recognition method is focused on checking the location of all stickers that belong on the left and right or front and back. First, the left and right corner sticker orientation is checked, then two additional corner stickers are checked to determine the COLL case (a recognition system called [[ATCRM]]). Then the left and right edges are found. This recognition method was developed by [[James Straughan | Michael James Straughan]].

[[image:ZBLL-Polar.png|300px|center]]

== Algorithms ==
* [https://web.archive.org/web/20031214235821/http://www.ai.univ-paris8.fr/~bhelmste/cube/solutions_567.html Bernard Helmstetter's original ZBLL algorithms, created for the Petrus method]
* [https://pepkin88.me/zbll-explorer/ pepkin88's ZBLL Explorer, compiles algorithms from many different resources]
* [http://lar5.com/cube/270/index.html Lars Petrus' One-look 2-alg ZBLL system]
* [http://bit.ly/ZBLLankidecks Anki Deck] - complete (2H and OH)
* Speedsolving.com: [http://www.speedsolving.com/forum/threads/bindedsas-algorithms.55518/ BindeDSA's Algorithms] - complete (2H and OH)
* Speedsolving.com: [http://www.speedsolving.com/forum/showthread.php?t=18172 Happy New Year! Also, ZBLL Algorithms] - complete
* [http://www-personal.umich.edu/~dlli/Hardwick/zbll.html Chris Hardwick's ZBLL algs] - incomplete
* [http://algdb.net/puzzle/333/zbll AlgDb Algorithms] - complete
* [https://archive.ph/tmQyo TaDing's algorithms] - 472/493 (OH)
* [https://www.speedcubingtips.eu/zbll-zborowski-bruchem-last-layer/ Speedcubingtips.eu ] - complete
* [https://docs.google.com/spreadsheets/d/1-uwmZHf4vwJxFgeB3-TiF8MQ0RFSS30d5CUK96PoIwk Juliette Sébastien's Algorithms] - complete (2H and OH)
* [https://cdn.discordapp.com/attachments/479068012637585419/482557378605088799/ZBLL.pdf&sa=D&ust=1589197725716000&usg=AFQjCNGpVwcFU50jZ4RgIvcwQPlHCd_onA Jack314's Algorithms] - complete
* [https://docs.google.com/spreadsheets/d/1uXwshDSwMPIxmAyrf40FxRNewGnlo8hTHHGQbHP8Mbk Tao Yu & Justin Taylor's Algorithms] - complete
* [https://docs.google.com/spreadsheets/d/1eva73qzgmnsqMsLZ89Uqc-UURb0MPWgRppTf-KmAgRs Brant Holbein's(Lazy Einstein) Algorithms] - full zz-a doc with ZBLL + AUF, ZZF2L(all 4 slots), FR slot WV and CLS(+ and -), and ZBLL recognition system.
* [https://docs.google.com/spreadsheets/d/1lERUMmQHtVcovzeTCCQx7iOe0ku_uIXGE2Snr-MZGAQ Nicolas Gertner's Algorithms] - complete
* [https://docs.google.com/spreadsheets/d/1ty7aLoEGTgJMKp_qqA-5nuPKBIWbV4tFmTej46k0GRw goodforthewin's Algorithms] - complete (2H and OH)
* [http://www.brookscubing.com/wp-content/uploads/2016/03/Anthony-Brooks-ZBLL.pdf Anthony Brooks' Algorithms] - excluding sunes

== Trainers ==

* [https://bestsiteever.ru/zbll/ Roman Strakhov's ZBLL trainer]
* [https://tao-yu.github.io/Alg-Trainer/ Tao Yu's trainer]

== Documentation ==
* [https://www.cubinghistory.com/3x3/Steps/ZBLL History of ZBLL on CubingHistory.com]
* [https://docs.google.com/spreadsheets/d/1nrrO2xaIHcI8EKaJUxj0PDzx4CJ58jqhsFDZSbxQaoQ/edit?gid=0#gid=0 Recognition system differences (by Ryan Hudgens)]
* Speedsolving.com: [http://www.speedsolving.com/forum/showthread.php?t=53675 Hierarchy of Last Layer Sub-Steps, Subsets of OLLCP and ZBLL]

== See also ==

* [[ZB Method]]
* [[ZBLS]]
* [[ZZ-a]]
* [[VH Method]]
* [http://www.speedsolving.com/wiki/index.php/Special:MediaWikiAlgDB?mode=view&view=default&puzzle=3&group=ZBLL-T ZBLL Algorithms] (complete set)
* [[H ZBLL]] (Algorithms)
* [[ZBLD]]
* [[OPLL]]

[[Category:3x3x3 last layer substeps]]
[[Category:Acronyms]]

File:ZBLL-Polar.png

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File:ZBLL-Straughan-Object.png

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Athefre:

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Athefre:

Face Turning Octahedron

2026-07-01T04:14:21Z

Athefre:

{{Puzzle Infobox|
|NAME=Face Turning Octahedron
|IMAGE=Dayan-fto-magnetic-ball-core-stickerless_540x.webp
|ALTERNATIVENAMES=FTO
|MECHANISM=Face Turning Octahedron
|SHAPE=Octahedron
|INVENTOR=David Pitcher
|YEAR=c. 2003
|COMPANIES=[[Dayan]], [[DianSheng]], [[LanLan]], [[Shengshou]], [[Qiyi]], [[Maru]]
|JAAPSCH=octaface}}

The Face Turning Octahedron is a three-layered face turning octahedral puzzle for which all three layers are the same width. The first working version was made by David Pitcher in the early 2000s and was later mass-produced by [[LanLan]]. In 2024, [[DianSheng]] released a magnetic version, which was followed by other speed versions by various companies including [[Dayan]], [[Qiyi]], and [[Shengshou]]. Before these versions were mass-produced, it was common to make one by attaching printed extentions to a Qiyi [[Rex Cube]].

== Basic Characteristics ==
The Face Turning Octahedron is a face-turning regular octahedral puzzle with a cut depth such that the cuts intersect at a point in the center of each face. It is the second shallowest possible planar cut depth of a face-turning octahedral puzzle (with the shallowest being the Dino Octahedron). Its pieces consist of 6 corners, 12 edges, and 24 X-centers. Since rotation about the faces of an octahedron result in two distinct sets of four faces each where a face from one set can never reach the starting position of any face from the other set, the stickers of an FTO are divided into two distinct orbits, where colors of adjacent faces can never end up on the same face. This means that the corners only have two possible orientations per location (when the puzzle is scrambled without cube rotations), the edges are always oriented, and there are two sets of X-centers that never mix. Interestingly, this also means than an FTO stickered with only four colors, with opposite sides having the same color, solves exactly the same way as an FTO stickered with all eight colors.

The corners turn out to be equivalent to pyraminx edges, which means that only even permutations are possible and that a single corner "flip" is impossible. Additionally, since each face turn does a 3-cycle of edges, only even permutations are possible for edges as well.

As calculated by Jaap, the FTO has a total of 31,408,133,379,194,880,000,000 visually distinct positions [https://www.jaapsch.net/puzzles/octaface.htm].

If the X-centers are to be each considered unique, then the number becomes [(6!/2)(2^6/2)(12!/2)(12!/2)^2]/12 = 13,188,400,838,457,446,891,520,000,000 total positions.

== Related Puzzles ==

=== Skewb Diamond ===

{{Main Article|Article=Skewb Diamond}}

[[Image:Skewb_diamond.png|120px]]

The Skewb Diamond, also known as the 2x2 FTO, can be seen as either a face-turning octahedron with deep cuts or a 2-layer version of the standard FTO. It is also an octahedral shape transformation of a [[Skewb]] where the Skewb's centers correspond to the Skewb Diamond's corners and the Skewb's corners correspond to the Skewb Diamond's centers, which means that orientation matters on the opposite pieces as compared to the standard Skewb.

=== Master FTO ===

[[Image:masterfto.png|120px]]

The Master FTO, or 4x4 FTO, is a four-layered face-turning octahedron with two different cut depths (one deep and one shallow) such that the faces appear like those of a [[Master Pyraminx]].

=== Other Related Puzzles ===

There are four distinct face-turning octahedral puzzles that each have a single planar cut depth. From shallowest to deepest, they are the Dino Octahedron, the standard FTO (the main subject of this article), the Master Skewb Diamond, and the Skewb Diamond (discussed above). The Dino Octahedron, briefly produced by MF8, is the shallowest possible face-turning octahedron with one cut per side. It is equivalent to a standard FTO with the addition of fixed centers. The Master Skewb Diamond is a face-turning octahedral puzzle with a cut depth between the standard FTO and the Skewb Diamond, and can be seen as a shape transformation of the Master Skewb. Although it has not yet been mass-produced in its pure form, MF8 has made a "crazy" version with added circular cuts on the faces. The only functional difference between the Dino Octahedron and the Master Skewb Diamond is that the centers are fixed on the Dino Octahedron, whereas they turn with the faces on the Master Skewb Diamond.

== Methods ==

There are many methods used to solve the Face Turning Octahedron, the most popular of which are described below.

=== Bencisco ===

The [[Bencisco method]] was created by Ben Streeter in 2020.

# First Block: Solve a block on the BL layer consisting of a large hexagon center and two triples. A triple is a corner and two opposite small triangle centers.
# Centers: Solve the remaining three hexagon centers in the layers to the right of the block built in the first step.
# Triple: Solve the triple at the upper left on the U layer.
# Last Three Triples: Finish the solve by forming the last three triples then solving them to their correct positions, or solve everything in a single step using 179 algorithms.

=== Nautilus ===

The [[Nautilus (FTO)|Nautilus method]] was developed by a team consisting of [[James Straughan]], Liam Highducheck, and Vincent Trang, with additional input by Ryan Hudgens and mrmangohands.

# First Block: Solve a block on the BL layer consisting of a large hexagon center and two triples.
# Centers: Solve the remaining three hexagon centers.
# Triple: Solve the last triple at the bottom right, completing the first two layers.
# Last Layer: Solve the last layer. This is typically accomplished by first solving the triangle centers then the corners, but other systems also exist such as OLL then PLL, or 1LLL.

There are some alternative steps to solving the first two layers that users may prefer:

# First Block: Solve a block on the BL layer consisting of a large hexagon center and two triples.
# Stripe: Solve the F2L stripe to the right of the first block. This leaves just the U and R layers unsolved.
# F2L: Solve the remainder of the F2L using just U and R turns.
# Last Layer: Solve the last layer.

=== Vertigo ===

By Ryan Hudgens and Ben Streeter.

# Vertex: Solve a corner and its surrounding four triangles and four edges.
# Second Vertex: Solve another vertex adjacent to the first. Keep these two at the bottom left of the first two layers.
# Edges and Triangles: Solve the last four edges and the two triangles at either the intersection of DR or UL.
# Last Six Triangles: If in the last step the two triangles at DR were solved, solve the three remaining U face triangles and the three that belong in the middle layer beneath the U layer, equivalent to the E layer on 3x3. Do the opposite of this if in the last step the two triangles at UL were solved.
# Last Three Triples: Finish the solve by forming the last three triples then solving them to their correct positions, or solve everything in a single step using 179 algorithms.

=== CFL ===

CFL is a method similar to CFOP and was created by James Straughan.

# Centers: Solve the three large hexagon centers around the sides of the first two layers.
# F2L: Solve the three triples of the first two layers.
# Last Layer: Solve the last layer. This is typically accomplished by first solving the triangle centers then the corners, but other systems also exist such as OLL then PLL or 1LLL.

Many CFOP techniques can be carried over such as pseudo slotting, edge control (corner control or triangle control in CFL), ZBLS (orienting corners or positioning triangles during the last slot), and XCross (arrow block + centers in CFL).

=== L4T Redux ===

A version of reduction that combines modern techniques with reduction to Pyraminx steps. All of the various Pyraminx steps can be incorporated into the method. The method was developed by Vincent Trang with assistance from James Straughan.

# First Block: Solve a block on the BL layer consisting of a large hexagon center and two triples. The two triples can be any triple and not just the ones that belong in those positions. This allows for more freedom in the reduction step.
# Centers: Solve the remaining three hexagon centers.
# Reduction: Form the last four triples using big cube style slicing techniques. This reduces the FTO to a Pyraminx stage.
# Pyra Stage: Solve as a Pyraminx.

=== Julian ===

# Center: Solve a large hexagon center.
# Arrow Blocks: Add two adjacent arrow blocks to the hexagon center.
# Third arrow: Solve the last arrow connected to the hexagon center, but leave out the two triangles that would go around the sides of the layer where the hexagon center is.
# Corners: Solve the last three corners.
# Triangles: Use commutators to solve all remaining small triangle centers.

== Tutorials/Guides ==
* [https://www.youtube.com/watch?v=6JT2tU00ccs Bencisco guide]
* [https://sites.google.com/view/nautilusfto Nautilus website]
* [https://sites.google.com/site/athefre/other-puzzles/cfl?authuser=0 CFL website]
* [https://docs.google.com/document/d/18CMTrFC9PYkEsheOHnywzvV0EdCb3SFGQXSK0DDb30o/edit?pli=1&tab=t.0 L4T Redux guide]
* [https://docs.google.com/spreadsheets/d/1_IHL077w-9U-qtpF9hvC6CrUn7etua5QgPH8vEMqK58/edit?usp=sharing L4T Redux L4E]

[[Category:Twisty puzzles]]

Face Turning Octahedron

2026-07-01T00:19:18Z

Athefre: /* L4T Redux */

{{Puzzle Infobox|
|NAME=Face Turning Octahedron
|IMAGE=Dayan-fto-magnetic-ball-core-stickerless_540x.webp
|ALTERNATIVENAMES=FTO
|MECHANISM=Face Turning Octahedron
|SHAPE=Octahedron
|INVENTOR=David Pitcher
|YEAR=c. 2003
|COMPANIES=[[Dayan]], [[DianSheng]], [[LanLan]], [[Shengshou]], [[Qiyi]], [[Maru]]
|JAAPSCH=octaface}}

The Face Turning Octahedron is a three-layered face turning octahedral puzzle for which all three layers are the same width. The first working version was made by David Pitcher in the early 2000s and was later mass-produced by [[LanLan]]. In 2024, [[DianSheng]] released a magnetic version, which was followed by other speed versions by various companies including [[Dayan]], [[Qiyi]], and [[Shengshou]]. Before these versions were mass-produced, it was common to make one by attaching printed extentions to a Qiyi [[Rex Cube]].

== Basic Characteristics ==
The Face Turning Octahedron is a face-turning regular octahedral puzzle with a cut depth such that the cuts intersect at a point in the center of each face. It is the second shallowest possible planar cut depth of a face-turning octahedral puzzle (with the shallowest being the Dino Octahedron). Its pieces consist of 6 corners, 12 edges, and 24 X-centers. Since rotation about the faces of an octahedron result in two distinct sets of four faces each where a face from one set can never reach the starting position of any face from the other set, the stickers of an FTO are divided into two distinct orbits, where colors of adjacent faces can never end up on the same face. This means that the corners only have two possible orientations per location (when the puzzle is scrambled without cube rotations), the edges are always oriented, and there are two sets of X-centers that never mix. Interestingly, this also means than an FTO stickered with only four colors, with opposite sides having the same color, solves exactly the same way as an FTO stickered with all eight colors.

The corners turn out to be equivalent to pyraminx edges, which means that only even permutations are possible and that a single corner "flip" is impossible. Additionally, since each face turn does a 3-cycle of edges, only even permutations are possible for edges as well.

As calculated by Jaap, the FTO has a total of 31,408,133,379,194,880,000,000 visually distinct positions [https://www.jaapsch.net/puzzles/octaface.htm].

If the X-centers are to be each considered unique, then the number becomes [(6!/2)(2^6/2)(12!/2)(12!/2)^2]/12 = 13,188,400,838,457,446,891,520,000,000 total positions.

== Related Puzzles ==

=== Skewb Diamond ===

{{Main Article|Article=Skewb Diamond}}

[[Image:Skewb_diamond.png|120px]]

The Skewb Diamond, also known as the 2x2 FTO, can be seen as either a face-turning octahedron with deep cuts or a 2-layer version of the standard FTO. It is also an octahedral shape transformation of a [[Skewb]] where the Skewb's centers correspond to the Skewb Diamond's corners and the Skewb's corners correspond to the Skewb Diamond's centers, which means that orientation matters on the opposite pieces as compared to the standard Skewb.

=== Master FTO ===

[[Image:masterfto.png|120px]]

The Master FTO, or 4x4 FTO, is a four-layered face-turning octahedron with two different cut depths (one deep and one shallow) such that the faces appear like those of a [[Master Pyraminx]].

=== Other Related Puzzles ===

There are four distinct face-turning octahedral puzzles that each have a single planar cut depth. From shallowest to deepest, they are the Dino Octahedron, the standard FTO (the main subject of this article), the Master Skewb Diamond, and the Skewb Diamond (discussed above). The Dino Octahedron, briefly produced by MF8, is the shallowest possible face-turning octahedron with one cut per side. It is equivalent to a standard FTO with the addition of fixed centers. The Master Skewb Diamond is a face-turning octahedral puzzle with a cut depth between the standard FTO and the Skewb Diamond, and can be seen as a shape transformation of the Master Skewb. Although it has not yet been mass-produced in its pure form, MF8 has made a "crazy" version with added circular cuts on the faces. The only functional difference between the Dino Octahedron and the Master Skewb Diamond is that the centers are fixed on the Dino Octahedron, whereas they turn with the faces on the Master Skewb Diamond.

== Methods ==

There are many methods used to solve the Face Turning Octahedron, the most popular of which are described below.

=== Bencisco ===

The [[Bencisco method]] was created by Ben Streeter in 2020.

# First Block: Solve a block on the BL layer consisting of a large hexagon center and two triples. A triple is a corner and two opposite small triangle centers.
# Centers: Solve the remaining three hexagon centers in the layers to the right of the block built in the first step.
# Triple: Solve the triple at the upper left on the U layer.
# Last Three Triples: Finish the solve by forming the last three triples then solving them to their correct positions, or solve everything in a single step using 179 algorithms.

=== Nautilus ===

The [[Nautilus (FTO)|Nautilus method]] was developed by a team consisting of [[James Straughan]], Liam Highducheck, and Vincent Trang, with additional input by Ryan Hudgens and mrmangohands.

# First Block: Solve a block on the BL layer consisting of a large hexagon center and two triples.
# Centers: Solve the remaining three hexagon centers.
# Triple: Solve the triple at the bottom left within the first two layers.
# Last Layer: Solve the last layer. This is typically accomplished by first solving the triangle centers then the corners, but other systems also exist such as OLL then PLL, or 1LLL.

There are some alternative steps to solving the first two layers that users may prefer:

# First Block: Solve a block on the BL layer consisting of a large hexagon center and two triples.
# Stripe: Solve the F2L stripe to the right of the first block. This leaves just the U and R layers unsolved.
# F2L: Solve the remainder of the F2L using just U and R turns.
# Last Layer: Solve the last layer.

=== Vertigo ===

By Ryan Hudgens and Ben Streeter.

# Vertex: Solve a corner and its surrounding four triangles and four edges.
# Second Vertex: Solve another vertex adjacent to the first. Keep these two at the bottom left of the first two layers.
# Edges and Triangles: Solve the last four edges and the two triangles at either the intersection of DR or UL.
# Last Six Triangles: If in the last step the two triangles at DR were solved, solve the three remaining U face triangles and the three that belong in the middle layer beneath the U layer, equivalent to the E layer on 3x3. Do the opposite of this if in the last step the two triangles at UL were solved.
# Last Three Triples: Finish the solve by forming the last three triples then solving them to their correct positions, or solve everything in a single step using 179 algorithms.

=== CFL ===

CFL is a method similar to CFOP and was created by James Straughan.

# Centers: Solve the three large hexagon centers around the sides of the first two layers.
# F2L: Solve the three triples of the first two layers.
# Last Layer: Solve the last layer. This is typically accomplished by first solving the triangle centers then the corners, but other systems also exist such as OLL then PLL or 1LLL.

Many CFOP techniques can be carried over such as pseudo slotting, edge control (corner control or triangle control in CFL), ZBLS (orienting corners or positioning triangles during the last slot), and XCross (arrow block + centers in CFL).

=== L4T Redux ===

A version of reduction that combines modern techniques with reduction to Pyraminx steps. All of the various Pyraminx steps can be incorporated into the method. The method was developed by Vincent Trang with assistance from James Straughan.

# First Block: Solve a block on the BL layer consisting of a large hexagon center and two triples. The two triples can be any triple and not just the ones that belong in those positions. This allows for more freedom in the reduction step.
# Centers: Solve the remaining three hexagon centers.
# Reduction: Form the last four triples using big cube style slicing techniques. This reduces the FTO to a Pyraminx stage.
# Pyra Stage: Solve as a Pyraminx.

=== Julian ===

# Center: Solve a large hexagon center.
# Arrow Blocks: Add two adjacent arrow blocks to the hexagon center.
# Third arrow: Solve the last arrow connected to the hexagon center, but leave out the two triangles that would go around the sides of the layer where the hexagon center is.
# Corners: Solve the last three corners.
# Triangles: Use commutators to solve all remaining small triangle centers.

== Tutorials/Guides ==
* [https://www.youtube.com/watch?v=6JT2tU00ccs Bencisco guide]
* [https://sites.google.com/view/nautilusfto Nautilus website]
* [https://sites.google.com/site/athefre/other-puzzles/cfl?authuser=0 CFL website]
* [https://docs.google.com/document/d/18CMTrFC9PYkEsheOHnywzvV0EdCb3SFGQXSK0DDb30o/edit?pli=1&tab=t.0 L4T Redux guide]
* [https://docs.google.com/spreadsheets/d/1_IHL077w-9U-qtpF9hvC6CrUn7etua5QgPH8vEMqK58/edit?usp=sharing L4T Redux L4E]

[[Category:Twisty puzzles]]

Face Turning Octahedron

2026-06-25T21:56:09Z

Athefre: /* L4T Redux */

Face Turning Octahedron

2026-06-25T18:02:41Z

Athefre: /* Nautilus */

Face Turning Octahedron

2026-06-25T18:02:04Z

Athefre:

NMCLL

2015-01-02T16:57:25Z

Athefre: /* External links */

{{Substep Infobox
|name=NMCLL
|image=NMCLL.png
|proposers=[[Gilles Roux]], [http://www.speedsolving.com/wiki/index.php?title=User:Athefre James Straughan]
|year=2004
|subgroup=
|algs=42
|moves=
|purpose=
* [[Speedsolving]]
* [[FMC]]
}}

'''NMCLL''' is the name given to the last layer of corners when the stickers don't match. Common methods that use this include [[Roux]], [[ZZ]], [[Petrus]], and [[CLL]] and [[EG]] for 2x2.

== Description ==
During a solve, it isn't initially required that the bottom layer of corners match. In Roux, for example, this gives four options for the second block. These pseudo blocks also have an effect on the last layer. More stickers from the F, B, and D layers can be mixed in. While any recognition can be used, the traditional ways are difficult to use with all non-matching corner types. A recognition method has been developed specifically to solve this problem and works equally well with matching and non-matching corners. All of the same algorithms can be used, though memorization of two patterns per algorithm is required. The use of this technique reduces the number of moves in the solve, which is especially useful for 2x2.

== See also ==
* [[CLL]]
* [[NMLL]]

== External links ==
* [https://sites.google.com/site/athefre/roux Athefre's Recognition Method]
* [http://www.speedsolving.com/forum/showthread.php?37073-2x2-Pseudo-Solving-Improving-CLL-and-EG&p=748779&viewfull=1#post748779 Guide for using with 2x2 CLL + EG]

[[Category:3x3x3 last layer substeps]]
[[Category:2x2x2 methods]]
[[Category:2x2x2 speedsolving methods]]
[[Category:2x2x2 substeps]]

NMLL

2014-07-19T14:18:50Z

Athefre:

{{Method Infobox
|name=NMLL
|image=NMLL.png
|proposers=James Straughan
|year=2010
|steps=2
|algs=56
|moves=18.77
|purpose=
* [[Speedsolving]]
}}

'''NMLL''' is an [[LL]] method to be used along with matching or non-matching blocks in methods that orient edges early (such as [[ZZ]] or [[Petrus]]). First, the colors that match the L and R centers are separated to opposite sides of the U-layer facing away from the U center. Then, the pieces are permuted into their correct places.

== See also ==
* [[COLL]]
* [[ZBLL]]

== External links ==
* [https://docs.google.com/spreadsheet/ccc?key=0AovQt1uV9t0sdFdhYzNHcl9OcHpBckRVa0wzVnU4c3c&hl=en_US#gid=0 Main Page]
* [https://docs.google.com/spreadsheet/ccc?key=0AovQt1uV9t0sdGduaEpGRTdaQ20xQk00c052UzNaOUE&hl=en_US#gid=0 Recognition Guide] Guide for recognizing Step 2.
* [http://www.speedsolving.com/forum/showthread.php?20834-ZZ-ZB-Home-Thread&p=723087&viewfull=1#post723087 Example Solves]

[[Category:3x3x3 last layer substeps]]
[[Category:Acronyms]]

Talk:NMCLL

2014-06-29T03:15:53Z

Athefre: Blanked the page

NMLL

2013-12-23T00:14:05Z

Athefre:

NMCLL

2013-09-27T21:31:54Z

Athefre: /* Description */

{{Method Infobox
|name=NMCLL
|image=NMCLL.png
|proposers=[[Gilles Roux]], [http://www.speedsolving.com/wiki/index.php?title=User:Athefre James Straughan]
|year=2004
|steps=1
|algs=42
|moves=
|purpose=
* [[Speedsolving]]
* [[FMC]]
}}

'''NMCLL''' is the name given to the last layer of corners when the stickers don't match. Common methods that use this include [[Roux]], [[ZZ]], [[Petrus]], and [[CLL]] and [[EG]] for 2x2.

== Description ==
During a solve, it isn't initially required that the bottom layer of corners match. In Roux, for example, this gives four options for the second block. These pseudo blocks also have an effect on the last layer. More stickers from the F, B, and D layers can be mixed in. While any recognition can be used, the traditional ways are difficult to use with all non-matching corner types. A recognition method has been developed specifically to solve this problem and works equally well with matching and non-matching corners. All of the same algorithms can be used, though memorization of two patterns per algorithm is required. The use of this technique reduces the number of moves in the solve, which is especially useful for 2x2.

== See also ==
* [[CLL]]
* [[NMLL]]

== External links ==
* [https://sites.google.com/site/athefre/roux Roux table]
* [http://www.speedsolving.com/forum/showthread.php?37073-2x2-Pseudo-Solving-Improving-CLL-and-EG&p=748779&viewfull=1#post748779 Guide for 2x2 use]

[[Category:3x3x3 last layer substeps]]
[[Category:2x2x2 methods]]
[[Category:2x2x2 speedsolving methods]]
[[Category:2x2x2 substeps]]

User:Athefre

2012-08-17T23:23:01Z

Athefre:

{{Infobox
|NAME=James Straughan
|IMAGE=
|IMAGEYEAR=visible
|ALIASES=
|COUNTRY=USA
|BIRTHDATE=June 21, 1988
|AGE=24
|JOBS=Hidden
|YEARSACTIVE=2005-present
|ID=
|FAMOUSFOR=Early Roux User
}}

Hello, I'm Athefre. I'm a Roux user since February 2006 and spend my time in #rubik and on method ideas.

== Community Interests ==
* Method history
* The further development of current and future methods

== Developments ==
* [[NMCLL]]
* [[NMLL]]
* [http://www.speedsolving.com/forum/showthread.php?38176-Roux-Misoriented-Centers-Table&p=772850&viewfull=1#post772850 Roux LSE 4a+4b Optimization]
* [http://www.speedsolving.com/forum/showthread.php?35293-CLL-Transformation-Table Corner Transformation]
* [http://www.speedsolving.com/forum/showthread.php?22862-Random-Cubing-Discussion&p=741058&viewfull=1#post741058 Edge Transformation]

{| align="center"
| valign="bottom" |{{Usr:Forums|ID=147}}
|}

Talk:NMCLL

2012-07-20T19:17:33Z

Athefre: Created page with "Note that, in this case, the Proposers category refers to those with the corner recognition method ideas. Gilles Roux for his original LR colors + U colors idea. James Strau..."

Note that, in this case, the Proposers category refers to those with the corner recognition method ideas. Gilles Roux for his original LR colors + U colors idea. James Straughan for his LR colors + 4 fixed stickers. Otherwise the proposer credit would have to be "Various" since pseudo blocks is a common idea that would be difficult to link to a single person.--[[User:Athefre|Athefre]] ([[User talk:Athefre|talk]]) 15:17, 20 July 2012 (EDT)

NMCMLL

2012-07-15T00:39:11Z

Athefre: Redirected page to NMCLL

#REDIRECT [[NMCLL]]

NMCLL

2012-07-12T23:22:21Z

Athefre:

{{Method Infobox
|name=NMCLL
|image=NMCLL.png
|proposers=[[Gilles Roux]], [http://www.speedsolving.com/wiki/index.php?title=User:Athefre James Straughan]
|year=2004
|steps=1
|algs=42
|moves=
|purpose=
* [[Speedsolving]]
* [[FMC]]
}}

'''NMCLL''' is the name given to the last layer of corners when the stickers don't match. Common methods that use this include [[Roux]], [[ZZ]], [[Petrus]], and [[CLL]] and [[EG]] for 2x2.

== Description ==
During a solve, it isn't initially required that the bottom layer of corners match. In Roux, for example, this gives four options for the second block. These pseudo blocks also have an effect on the last layer. More stickers from the F, B, and D layers can be mixed in. While any recognition can be used, the traditional ways are difficult to use with all non-matching corner types. A recognition method has been developed specifically to solve this problem and works equally well with matching and non-matching corners. All of the same algorithms can be used, though memorization of two patterns per algorithm is required. Because of this, current CLL users are reluctant to relearn recognition and most Roux users almost exclusively use matching or opposite blocks.

== See also ==
* [[CLL]]
* [[NMLL]]

== External links ==
* [https://sites.google.com/site/athefre/roux Roux table]
* [http://www.speedsolving.com/forum/showthread.php?37073-2x2-Pseudo-Solving-Improving-CLL-and-EG&p=748779&viewfull=1#post748779 Guide for 2x2 use]

[[Category:3x3x3 last layer substeps]]
[[Category:2x2x2 methods]]
[[Category:2x2x2 speedsolving methods]]
[[Category:2x2x2 substeps]]

NMCLL

2012-07-12T23:19:12Z

Athefre:

{{Method Infobox
|name=NMCLL
|image=NMCLL.png
|proposers=[[Gilles Roux]], [http://www.speedsolving.com/wiki/index.php?title=User:Athefre James Straughan]
|year=2004
|steps=1
|algs=42
|moves=
|purpose=
* [[Speedsolving]]
* [[FMC]]
}}

'''NMCLL''' is the name given to the last layer of corners when the stickers don't match. Common methods that use this include [[Roux]], [[ZZ]], [[Petrus]], and [[CLL]] and [[EG]] for 2x2.

== Description ==
During a solve, it isn't initially required that the bottom layer of corners match. In Roux, for example, this gives four options for the second block. These pseudo blocks also have an effect on the last layer. More stickers from the F, B, and D layers can be mixed in. While any recognition can be used, the traditional ways are difficult to use with all non-matching corner types. A recognition method has been developed specifically to solve this problem and works equally well with matching and non-matching corners. All of the same algorithms can be used, though memorization of two patterns per algorithm is required. Because of this, current CLL users are reluctant to relearn recognition and most Roux users almost exclusively use matching or opposite blocks.

== See also ==
* [[CLL]]
* [[NMLL]]

== External links ==
* [https://sites.google.com/site/athefre/roux Roux table]
* [http://www.speedsolving.com/forum/showthread.php?37073-2x2-Pseudo-Solving-Improving-CLL-and-EG Guide for 2x2 use]

[[Category:3x3x3 last layer substeps]]
[[Category:2x2x2 methods]]
[[Category:2x2x2 speedsolving methods]]
[[Category:2x2x2 substeps]]

LSE

2012-07-10T03:27:26Z

Athefre:

{{Method Infobox
|name=Last Six Edges
|image=Roux_method.gif
|proposers=[[Gilles Roux]]
|year=2003
|anames=LSE, L6E
|variants=[[ELL]], [[L5E]]
|steps=1
|moves=
|purpose=
* [[Speedsolving]]
}}

'''Last Six Edges''' (abbreviated '''LSE''' or '''L6E''') is a possible last [[step]] in 3x3 speedsolving that solves the M-slice centers and edges (UF, UB, DF, DB) together with UL and UR edges. It is the last step of the [[Roux Method]] and the [[Ortega Method]].

== Possible Approaches ==
LSE can be solved in various ways; [[Gilles Roux]] himself, the inventer of the Roux Method, advocates a flexible/semi-intuitive approach to LSE without a strict division into substeps. The optimal approach is likely a combination of the approaches below.

'''Layers-Based Approach'''
* 1. centers, BD, and FD
* 2. [[ELL]]
This layer-based approach seems out of place in any method ending with LSE.

'''Original Roux'''
* 1. Orient centers and edges
* 2. Permute UR and UL edges
* 3. Permute the M slice

The following two approaches are commonly used in [[Corners first]] methods.

'''Corners First Approach 1'''
* 1. Solve UL or UR
* 2. Insert UL/UR while orienting the M slice
* 3. Permute the M slice

'''Corners First Approach 2'''
* 1. Solve both UL and UR
* 2. Orient and permute the M slice

Reduction to L5E has been proposed as an experimental approach.

'''L5E'''
* 1. Centers and BD
* 2. [[L5E]]

== External links ==
* [http://grrroux.free.fr/method/Step_4.html Standard Method]
* [http://rubikscube.info/lastsix2look.html 2.5 Look]
* [http://www.speedsolving.com/forum/showthread.php?37658-Roux-method-An-alternate-way-of-solving-the-last-6-edges&p=760583&viewfull=1#post760583 Robert Yau's Alternative]
* [http://www.speedsolving.com/forum/showthread.php?9095-Playing-With-Roux-Orientations UL/UR to DF/DB Method]
* [http://www.speedsolving.com/forum/showthread.php?23916-2-step-finish-for-Roux-Edges Two Step Method]
* [http://www.speedsolving.com/forum/showthread.php?35350-Roux-4b-to-4c-Transition Roux 4b-4c Transition]

[[Category:3x3x3 other substeps]]

LSE

2012-07-10T03:23:53Z

Athefre: /* External links */

{{Method Infobox
|name=Last Six Edges
|image=Roux_method.gif
|proposers=[[Gilles Roux]]
|year=2003
|anames=LSE, L6E
|variants=[[ELL]], [[L5E]]
|steps=1
|moves=
|purpose=
* [[Speedsolving]]
}}

'''Last Six Edges''' (abbreviated '''LSE''' or '''L6E''') is a possible last [[step]] in 3x3 speedsolving that solves the M-slice centers and edges (UF, UB, DF, DB) together with UL and UR edges. It is the last step of the [[Roux Method]] and the [[Ortega Method]].

== Possible Approaches ==
LSE can be solved in various ways; [[Gilles Roux]] himself, the inventer of the Roux Method, advocates a flexible/semi-intuitive approach to LSE without a strict division into substeps. The optimal approach is likely a combination of the approaches below.

'''Layers-Based Approach'''
* 1. centers, BD, and FD
* 2. [[ELL]]
This layer-based approach seems out of place in any method ending with LSE.

'''Original Roux'''
* 1. Orient centers and edges
* 2. Permute UR and UL edges
* 3. Permute the M slice

The following two approaches are commonly used in [[Corners first]] methods.

'''Corners First Approach 1'''
* 1. Solve UL or UR
* 2. Insert UL/UR while orienting the M slice
* 3. Permute the M slice

'''Corners First Approach 2'''
* 1. Solve both UL and UR
* 2. Orient and permute the M slice

Reduction to L5E has been proposed as an experimental approach.

'''L5E'''
* 1. Centers and BD
* 2. [[L5E]]

== External links ==
* [http://grrroux.free.fr/method/Step_4.html Standard Method]
* [http://rubikscube.info/lastsix2look.html 2.5 Look]
* [http://www.speedsolving.com/forum/showthread.php?37658-Roux-method-An-alternate-way-of-solving-the-last-6-edges&p=760583 Robert Yau's Alternative]
* [http://www.speedsolving.com/forum/showthread.php?9095-Playing-With-Roux-Orientations UL/UR to DF/DB Method]
* [http://www.speedsolving.com/forum/showthread.php?23916-2-step-finish-for-Roux-Edges Two Step Method]
* [http://www.speedsolving.com/forum/showthread.php?35350-Roux-4b-to-4c-Transition Roux 4b-4c Transition]

[[Category:3x3x3 other substeps]]

Roux method

2012-07-09T18:27:20Z

Athefre: /* Improvement */

{{Method Infobox
|name=Roux
|image=Roux_method.gif
|proposers=[[Gilles Roux]]
|year=2003
|anames
|variants
|steps=4
|algs=9-42
|moves=[[Speedsolving|Speed]]:48, [[FM]]:28-
|purpose=
* [[Speedsolving]]
* [[Fewest Moves]]
}}

The '''Roux Method''' (French pronunciation: [ʁu]) is a 3x3 speedsolving method invented by [[Gilles Roux]]. Unlike the [[Fridrich]] and [[Petrus]] methods, the inventor of this method has used it to achieve an official sub-15 average. Similarities can be drawn to the Petrus method's block building and the [[Waterman method]]'s layer-on-the-left and edges-last aspects.

==The Steps==

1. Build a 1x2x3 block anywhere on the cube.

2. Build a second 1x2x3 block opposite of the first 1x2x3 block, without disrupting the first 1x2x3 block. After this step, there should be two 1x2x3 blocks: one on the lower left side, and one lower right side, leaving the U slice and M slice free to move.

3. Simultaneously [[orient]] and [[permute]] the remaining 4 corners on the top layer (U-slice). You can use [[CMLL]],[[COLL]], or Corner OLL's (along with T and Y permutation) to do this.

4. [[Orient]] the 6 remaining edges (UF, UB, UL, UR, DF, DB need to be oriented correctly).

5. Solve the left and right layer edges. After this step, both the left and right side layers should be complete.

6. Solve the centers and edges in the M slice, ''see [[Last Six Edges]]''.

: ''See also: [[L5E]]''

==Pros==

Like the Petrus method, the Roux method uses fewer moves than the popular Fridrich method. It is also more intuitive and requires fewer algorithms. After the first block is built the rest of the cube can be solved mostly with R, r, M and U moves thus eliminating rotations.

==Cons==

Block building can be difficult for a beginner to get used to. The reliance on r and M moves may also be difficult for some people, so much so that cubers who have trouble with M turns should probably not use this as their main method (or better, practice practice practice the M moves). Slice turns can also be slower than using a [[quarter-turn metric]].

==Improvement==

Some Roux users have learned multiple algorithms for each CLL case, each affecting edges in a different way. This allows for manipulation of edge orientation, leading to an easier LSE.

Possibly another improvement is to expand to solving any of the four second blocks. This means that the D-layer colors of the two blocks don't have to match. One negative, if someone has already learned a recognition method for CLL, is that to easily use the full range of second block options, a switch to [[NMCLL]] recognition is necessary. Another is that LSE EO is a bit more difficult to recognize in some solves.

== Notable Users ==
* [[Gilles Roux]] [http://www.worldcubeassociation.org/results/p.php?i=2004ROUX01]
* [[Thom Barlow]] (Kirjava) [http://www.worldcubeassociation.org/results/p.php?i=2006BARL01]
* [[Austin Moore]] (BigGreen) [http://www.worldcubeassociation.org/results/p.php?i=2009MOOR01]
* [[Jules Manalang]] (Waffo) [http://www.worldcubeassociation.org/results/p.php?i=2008MANA02]
* [[Alexander Lau]] (5BLD) [http://www.worldcubeassociation.org/results/p.php?i=2011LAUA01]
== External links ==
* [http://grrroux.free.fr/method/Intro.html Gilles Roux's tutorial]
* [http://wafflelikescubes.webs.com/ Waffle's Roux Site]
* Wikia: [http://rubiks.wikia.com/wiki/Roux_Method Roux Method]
* [http://www.speedsolving.com/forum/showthread.php?t=11506 Waffle's Roux Tutorial]
* [http://rouxtorial.webs.com/ 5BLD's and PandaCuber's Roux Tutorial]
* [http://www.speedsolving.com/forum/showthread.php?29123-The-reconstruction-thread&p=634675&viewfull=1#post634675 Reconstruction for BigGreen's unofficial Ao5 9.51]
* [http://games.groups.yahoo.com/group/speedsolvingrubikscube/message/5923 Original Method Proposal]

[[Category:3x3x3 methods]]
[[Category:3x3x3 Speedsolving Methods]]
[[Category:Fewest Moves Methods]]

Roux method

2012-07-08T16:41:23Z

Athefre:

{{Method Infobox
|name=Roux
|image=Roux_method.gif
|proposers=[[Gilles Roux]]
|year=2003
|anames
|variants
|steps=4
|algs=9-42
|moves=[[Speedsolving|Speed]]:48, [[FM]]:28-
|purpose=
* [[Speedsolving]]
* [[Fewest Moves]]
}}

The '''Roux Method''' (French pronunciation: [ʁu]) is a 3x3 speedsolving method invented by [[Gilles Roux]]. Unlike the [[Fridrich]] and [[Petrus]] methods, the inventor of this method has used it to achieve an official sub-15 average. Similarities can be drawn to the Petrus method's block building and the [[Waterman method]]'s layer-on-the-left and edges-last aspects.

==The Steps==

1. Build a 1x2x3 block anywhere on the cube.

2. Build a second 1x2x3 block opposite of the first 1x2x3 block, without disrupting the first 1x2x3 block. After this step, there should be two 1x2x3 blocks: one on the lower left side, and one lower right side, leaving the U slice and M slice free to move.

3. Simultaneously [[orient]] and [[permute]] the remaining 4 corners on the top layer (U-slice). You can use [[CMLL]],[[COLL]], or Corner OLL's (along with T and Y permutation) to do this.

4. [[Orient]] the 6 remaining edges (UF, UB, UL, UR, DF, DB need to be oriented correctly).

5. Solve the left and right layer edges. After this step, both the left and right side layers should be complete.

6. Solve the centers and edges in the M slice, ''see [[Last Six Edges]]''.

: ''See also: [[L5E]]''

==Pros==

Like the Petrus method, the Roux method uses fewer moves than the popular Fridrich method. It is also more intuitive and requires fewer algorithms. After the first block is built the rest of the cube can be solved mostly with R, r, M and U moves thus eliminating rotations.

==Cons==

Block building can be difficult for a beginner to get used to. The reliance on r and M moves may also be difficult for some people, so much so that cubers who have trouble with M turns should probably not use this as their main method (or better, practice practice practice the M moves). Slice turns can also be slower than using a [[quarter-turn metric]].

==Improvement==

Some Roux users have learned multiple algorithms for each CLL case, each affecting edges in a different way. This allows for manipulation of edge orientation, leading to an easier LSE.

Possibly another improvement is to expand to solving any of the four second blocks. This means that the D-layer colors of the two blocks don't have to match. One negative, if someone has already learned a recognition method for CMLL, is that to easily use the full range of second block options, a switch to [[NMCLL]] recognition is necessary. Another is that blocks not matching makes LSE EO difficult to recognize in 50% of solves.

== Notable Users ==
* [[Gilles Roux]] [http://www.worldcubeassociation.org/results/p.php?i=2004ROUX01]
* [[Thom Barlow]] (Kirjava) [http://www.worldcubeassociation.org/results/p.php?i=2006BARL01]
* [[Austin Moore]] (BigGreen) [http://www.worldcubeassociation.org/results/p.php?i=2009MOOR01]
* [[Jules Manalang]] (Waffo) [http://www.worldcubeassociation.org/results/p.php?i=2008MANA02]
* [[Alexander Lau]] (5BLD) [http://www.worldcubeassociation.org/results/p.php?i=2011LAUA01]
== External links ==
* [http://grrroux.free.fr/method/Intro.html Gilles Roux's tutorial]
* [http://wafflelikescubes.webs.com/ Waffle's Roux Site]
* Wikia: [http://rubiks.wikia.com/wiki/Roux_Method Roux Method]
* [http://www.speedsolving.com/forum/showthread.php?t=11506 Waffle's Roux Tutorial]
* [http://rouxtorial.webs.com/ 5BLD's and PandaCuber's Roux Tutorial]
* [http://www.speedsolving.com/forum/showthread.php?29123-The-reconstruction-thread&p=634675&viewfull=1#post634675 Reconstruction for BigGreen's unofficial Ao5 9.51]
* [http://games.groups.yahoo.com/group/speedsolvingrubikscube/message/5923 Original Method Proposal]

[[Category:3x3x3 methods]]
[[Category:3x3x3 Speedsolving Methods]]
[[Category:Fewest Moves Methods]]

Ernő Rubik

2012-07-08T00:15:01Z

Athefre:

{{Infobox
|NAME=Ernő Rubik
|IMAGE=Erno Rubik.jpg
|IMAGEYEAR=
|ALIASES=
|COUNTRY=Hungary
|BIRTHDATE=July 13, 1944
|AGE=66
|JOBS=Inventor, Designer
|YEARSACTIVE=1974-present
|FAMOUSFOR=Invention of the 3x3x3 Cube
}}
'''Ernő Rubik''', or according to the Eastern order naming convention, '''Rubik Ernő''' (Hungarian pronunciation: ['ɛrnøː 'rubik]), is the [[Hungary|Hungarian]] inventor of the [[Rubik's cube]] and many other [[puzzle]]s and toys. As a professor of architecture, he invented the cube as a teaching tool.

== External Links ==
* YouTube: [http://www.youtube.com/watch?v=0poQ8q8RzSg Creator of the Cube: Erno Rubik]
* [http://www.puzzlesolver.com/puzzle.php?id=29;page=15 The Perplexing Life of Erno Rubik]
* [http://games.groups.yahoo.com/group/speedsolvingrubikscube/message/4447 His Method (Unconfirmed)]

[[Category:Puzzle inventors|Rubik, Ernő]]
[[Category:Cubers|Rubik, Ernő]]

NMCLL

2012-07-07T20:47:00Z

Athefre:

{{Method Infobox
|name=NMCLL
|image=NMCLL.png
|proposers=[[Gilles Roux]], [http://www.speedsolving.com/wiki/index.php?title=User:Athefre James Straughan]
|year=2004
|steps=1
|algs=42
|moves=
|purpose=
* [[Speedsolving]]
* [[FMC]]
}}

'''NMCLL''' is the name given to the last layer of corners when the pieces don't match. While any recognition can be used, the traditional ways are difficult to use with all non-matching corner types. A recognition method has been developed specifically to solve this problem and works equally well with matching and non-matching corners. All of the same algorithms can be used, though memorization of two patterns per algorithm is required. Because of this, current CLL users are reluctant to relearn recognition and most [[Roux]] users almost exclusively use matching or opposite blocks. Currently, full NMCLL is more easily applied to 2x2 methods, such as CLL and EG, where the move count benefit makes much more of a difference.

== See also ==
* [[CLL]]
* [[NMLL]]

== External links ==
* [http://www.speedsolving.com/forum/showthread.php?37073-2x2-Pseudo-Solving-Improving-CLL-and-EG Guide for 2x2 use]

[[Category:3x3x3 last layer substeps]]
[[Category:2x2x2 methods]]
[[Category:2x2x2 speedsolving methods]]
[[Category:2x2x2 substeps]]

Roux method

2012-07-07T20:16:05Z

Athefre:

{{Method Infobox
|name=Roux
|image=Roux_method.gif
|proposers=[[Gilles Roux]]
|year=2003
|anames
|variants
|steps=4
|algs=9-42
|moves=[[Speedsolving|Speed]]:48, [[FM]]:28-
|purpose=
* [[Speedsolving]]
* [[Fewest Moves]]
}}

The '''Roux Method''' (French pronunciation: [ʁu]) is a 3x3 speedsolving method invented by [[Gilles Roux]]. Unlike the [[Fridrich]] and [[Petrus]] methods, the inventor of this method has used it to achieve an official sub-15 average. Similarities can be drawn to the Petrus method's block building and the [[Waterman method]]'s layer-on-the-left and edges-last aspects.

==The Steps==

1. Build a 1x2x3 block anywhere on the cube.

2. Build a second 1x2x3 block opposite of the first 1x2x3 block, without disrupting the first 1x2x3 block. After this step, there should be two 1x2x3 blocks: one on the lower left side, and one lower right side, leaving the U slice and M slice free to move.

3. Simultaneously [[orient]] and [[permute]] the remaining 4 corners on the top layer (U-slice). You can use [[CMLL]],[[COLL]], or Corner OLL's (along with T and Y permutation) to do this.

4. [[Orient]] the 6 remaining edges (UF, UB, UL, UR, DF, DB need to be oriented correctly).

5. Solve the left and right layer edges. After this step, both the left and right side layers should be complete.

6. Solve the centers and edges in the M slice, ''see [[Last Six Edges]]''.

: ''See also: [[L5E]]''

==Improvement==

Some Roux users have learned multiple algorithms for each CLL case, each affecting edges in a different way. This allows for manipulation of edge orientation, leading to an easier LSE.

Possibly another improvement is to expand to solving any of the four second blocks. This means that the D-layer colors of the two blocks don't have to match. One negative, if someone has already learned a recognition method for CMLL, is that to easily use the full range of second block options, a switch to [[NMCLL]] recognition is necessary. Another is that blocks not matching makes LSE EO difficult to recognize in 50% of solves.

==Pros==

Like the Petrus method, the Roux method uses fewer moves than the popular Fridrich method. It is also more intuitive and requires fewer algorithms. After the first block is built the rest of the cube can be solved mostly with R, r, M and U moves thus eliminating rotations.

==Cons==

Block building can be difficult for a beginner to get used to. The reliance on r and M moves may also be difficult for some people, so much so that cubers who have trouble with M turns should probably not use this as their main method (or better, practice practice practice the M moves). Slice turns can also be slower than using a [[quarter-turn metric]].

== Notable Users ==
* [[Gilles Roux]] [http://www.worldcubeassociation.org/results/p.php?i=2004ROUX01]
* [[Thom Barlow]] (Kirjava) [http://www.worldcubeassociation.org/results/p.php?i=2006BARL01]
* [[Austin Moore]] (BigGreen) [http://www.worldcubeassociation.org/results/p.php?i=2009MOOR01]
* [[Jules Manalang]] (Waffo) [http://www.worldcubeassociation.org/results/p.php?i=2008MANA02]
* [[Alexander Lau]] (5BLD) [http://www.worldcubeassociation.org/results/p.php?i=2011LAUA01]
== External links ==
* [http://grrroux.free.fr/method/Intro.html Gilles Roux's tutorial]
* [http://wafflelikescubes.webs.com/ Waffle's Roux Site]
* Wikia: [http://rubiks.wikia.com/wiki/Roux_Method Roux Method]
* [http://www.speedsolving.com/forum/showthread.php?t=11506 Waffle's Roux Tutorial]
* [http://rouxtorial.webs.com/ 5BLD's and PandaCuber's Roux Tutorial]
* [http://www.speedsolving.com/forum/showthread.php?29123-The-reconstruction-thread&p=634675&viewfull=1#post634675 Reconstruction for BigGreen's unofficial Ao5 9.51]
* [http://games.groups.yahoo.com/group/speedsolvingrubikscube/message/5923 Original Method Proposal]

[[Category:3x3x3 methods]]
[[Category:3x3x3 Speedsolving Methods]]
[[Category:Fewest Moves Methods]]