Speedsolving.com Wiki - User contributions [en]

Tripod Method

2026-06-23T19:46:05Z

Hiori Fembysolver: Complete overhaul and expansion of the article.

{{Method Infobox
|name=Tripod
|image=Tripod_method.gif
|proposers=[[Ryan Heise]], [[Michael Gottlieb]], [[Mirek Goljan]]
|year=2002
|anames
|variants= [[Petrus]], [[ZZ]]-Tripod
|steps=4
|algs=58
|moves= ~50
|purpose= [[Speedsolving]]
}}

A blockbuilding approach to solving the 3x3x3, first proposed by [[Ryan Heise]] and developed by [[Michael Gottlieb]] and [[Mirek Goljan]]. The method is characterized by its unique endgame state, which involves building a 2x2x1 block on the Last Layer to isolate the remaining unsolved pieces into a 5-piece "tripod" structure.

== The Steps ==
The Tripod method transitions smoothly from highly free-form intuitive blockbuilding into a highly specialized, low-movecount algorithmic endgame. The standard execution consists of the following phases:

=== Step 1: 2x2x2 Block ===
The solver intuitively constructs a 2x2x2 block in any corner of the cube. This step is identical to the beginning of the [[Petrus]] method. Because Tripod can be executed with full color neutrality, solvers typically take advantage of the 15-second inspection time to plan the most efficient block possible.
* '''Average Move Count:''' 6–8 moves.

=== Step 2: Block Expansion (F2L-1) ===
The initial 2x2x2 block is systematically expanded by attaching three separate 1x2x2 blocks adjacent to it. This process builds up the structure of the first two layers intuitively. Unlike CFOP, which relies strictly on rigid slotting, this phase allows for highly creative, multi-dimensional extensions across multiple faces.
* '''Average Move Count:''' ~15–18 moves.

=== Step 3: Last F2L Slot & LL Block Formation ===
Instead of completing the traditional First Two Layers (F2L) directly, the solver manipulates the remaining pieces to build a 2x2x1 block directly onto the Last Layer. By doing this, the final F2L slot is completed while simultaneously solving a portion of the Last Layer (1 corner and 2 edges), restricting the final unsolved state to just 5 pieces.
* '''Average Move Count:''' ~8–10 moves.

=== Step 4: Tripod Last Layer (TLL) ===
The final phase addresses the remaining 5 unsolved pieces of the cube (3 corners and 2 edges). Using a single algorithm from a pool of '''58 cases''' (or 51 if edges are consistently pre-oriented), the solver completely permutes and orients the remaining elements to finish the entire cube.
* '''Average Move Count:''' ~12 moves.

== Variants ==
* '''[[ZZ]]-Tripod:''' ZZ-Tripod, invented by Neuro in 2017, is an attempt at combining [[ZZ]] with Tripod, resulting in a normal ZZ solve up to F2L-1 when a 1x2x2 block is built on the top face. This is followed by NLS to insert the last F2L pair while preserving edge orientation. After that, the last layer is solved using TELL, which is a subset of both [[Tripod LL]] and [[ZBLL]] with very few algorithms.

== Recognition and TLL Strategy ==
The endgame of Tripod relies entirely on identifying the state of the 5 remaining pieces (3 corners and 2 edges) relative to the already completed 2x2x1 block on the top layer.

Solvers often divide the 58 cases into subsets based on:
* '''Edge Orientation (EO):''' Determining whether the remaining 2 edges are oriented or misoriented. If edges are actively oriented during Step 3, the total algorithm count drops from 58 down to 51 cases.
* '''Corner Permutation:''' Tracking the relationship between the 3 unsolved corners to determine the correct permutation variant.

Advanced practitioners may initially solve TLL in two looks (solving Edges first using commutators, followed by Corners) as a transitional phase before memorizing the full 1-look algorithmic database.

== Pros & Cons ==

{| class="wikitable" style="width:100%;"
! style="background:#d5e8d4; width:50%;" | Pros
! style="background:#f8cecc; width:50%;" | Cons
|-
| valign="top" |
* '''High Move Efficiency:''' Like many other blockbuilding approaches, this method uses fewer moves than the ever-popular CFOP method.
* '''Good Lookahead:''' The steps are all fairly simple and easy to execute, allowing for good lookahead throughout the solve.
* '''Low Algorithm Density:''' The method has a low algorithm count compared to most mainstream methods such as CFOP or ZZ.
| valign="top" |
* '''Restrictive Turning:''' The blocks, particularly the U layer block, are quite restrictive to the construction of the final F2L slot.
* '''Difficult Recognition:''' Recognition for the final step is not excellent and could be compared to that of [[COLL]].
* '''Steep Learning Curve:''' Beginners may find the intuitive nature of blockbuilding to be difficult compared to layer-by-layer methods.
|-
|}

== Example solve ==

Scramble (white on top, green in front): L' F2 R U B R2 D' F2 L' B U' R2 F2 B2 U L2 U' R2 L2

x2 R U' D R' D' - 2x2x2

y' L' F U' F2 L F' - First 2x2x1 block

L2 D L' U2 L D' - Second 2x2x1 block

U F R U' R' F' L' U' L U2 - Final 2x2x1 block

U' R F' U' F' U F R' F2 U' F2 U2 - F2L slot

L' U R U' R' U R U' R' L R U R' U' R U R' U' - Last 5 pieces

== External links ==
* [http://web.mac.com/teisenmann/Tripod/main.html Web-based tutorial]
* [http://www.ws.binghamton.edu/fridrich/L1/ece.htm Mirek Goljan's tripod algorithms]
* [http://games.groups.yahoo.com/group/speedsolvingrubikscube/message/2234 Ryan Heise's Post]
* [https://mzrg.com/rubik/methods/tripod/ Michael Gottlieb's explanation]
* [https://docs.google.com/spreadsheets/d/1dPeO6UkCF4QsyineVvHr6wZOcBkVmfTZnMA42KM92to Neuro's ZZ-Tripod algorithms (includes NLS and TELL)]
* YouTube: [https://youtu.be/nMlEQ9M6Xcg Neuro's ZZ-Tripod tutorial]
* Speedsolving.com: [http://www.speedsolving.com/forum/threads/bindedsas-algorithms.55518/ BindeDSA's Algorithms]
* [https://www.youtube.com/watch?v=fSBz4d4dDMk Tripod as a beginner method - Video tutorial]
* [https://docs.google.com/spreadsheets/d/e/2PACX-1vSFMcGiT6SFKFYAyleJSVEhSiO0NL3lhXH6vvNZNgpc7Hf7E41EbyUtcpN81uibvURZ8nWjuAGo7_YO/pubhtml ZBLL Tripod v1.5]

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

Zeta-Bp8

2026-06-19T19:25:35Z

Hiori Fembysolver: /* See Also */

{| class="wikitable" style="float:right; width:280px; margin-left:15px; font-size:95%; border: 1px solid #a2a9b1;"
|-
! colspan="2" style="background:#b3c6ff; text-align:center; font-size:115%; padding:8px;" | Zeta-Bp8 Method
|-
| '''Creator:''' || Bernardo Pietro (Hiori)
|-
| '''Type:''' || Hybrid Blockbuilding / Algorithmic
|-
| '''Steps:''' || 3 (Zeta Slotting, CMLL, 1-Look L8E)
|-
| '''Move Count:''' || 43-50 (Average)
|-
| '''Year:''' || 2026
|-
| '''Key Feature:''' || Pure Outer-Layer Endgame (Slice-Free)
|}

'''Zeta-Bp8''' is an advanced color-neutral 3x3 speedcubing method developed by '''Hiori (Bernardo Pietro)'''. The method is designed to maximize movement efficiency through intuitive blockbuilding while transitioning into a high-TPS, slice-free endgame.

The defining characteristic of Zeta-Bp8 is its total rejection of internal slice moves (M, S, and E) during the final stages of the solve. By utilizing a "Pure Outer-Layer" approach, the method eliminates mechanical lockups and allows solvers to maintain maximum turning speed during the Last 8 Edges (L8E) phase.

== Philosophical Approach ==
Zeta-Bp8 bridges the gap between the intuitive efficiency of [[Roux]] and the algorithmic reliability of [[CFOP]]. It treats the cube not as a series of layers, but as a structure of "Good" and "Bad" edges that dictate the most ergonomic path to completion.

== Comparison to Columns First Methods ==
While Zeta BP8 shares surface-level similarities with classic Columns First methods (such as [[Waterman Method]] or [[Roux Method]]) due to its early focus on corner resolution, the underlying philosophy and execution differ significantly:
* '''Blockbuilding vs. Column Structure:''' Columns First methods typically require building distinct vertical columns before solving the remaining pieces. Zeta BP8, on the other hand, utilizes a unique approach that transitions into a highly optimized Last Slot and Last Layer (LS/LL) state, reducing transitions and maintaining high TPS (Turns Per Second).
* '''Algorithmic Efficiency:''' Unlike older Columns First variants that rely heavily on intuitive piece-by-piece tracking or restricted layer movements, Zeta leverages a streamlined algorithmic endgame consisting of [[CMLL]] and a specialized slice-free 1-Look L8E sequence to guarantee efficient, low-movecount finishes.
* '''Ergonomics:''' Traditional Columns First solving often demands frequent M-slice moves or awkward cube rotations early on. Zeta BP8 prioritizes modern fingertrick ergonomics, allowing solvers to utilize standard <R, U, F> Gen movements more naturally throughout the solve.

== Step 1: Zeta Slotting ==
[[File:Zeta_Bp8_Step1.png|thumb|right|300px|State after Zeta Slotting: Lower blocks and slots completed, isolating corners and edges.]]
The foundational stage of the method focuses on building the lower structure of the cube using full color neutrality. Instead of a fixed cross, the solver builds blocks and slots dynamically.

=== Edge Classification System ===
The efficiency of this step relies on the solver's ability to classify edges during the 15-second inspection:
* '''Good Edges:''' Edges that can be oriented and solved in 3 moves or less.
* '''Bad Edges:''' Edges that require 4 or more moves to be solved.

The solver manipulates these pieces to ensure the most ergonomic flow, utilizing active lookahead to track corner positions while the final slots are being inserted.

* '''Average Move Count:''' ~18 moves.

== Step 2: CMLL (Corners of the Last Layer) ==
[[File:Zeta_Bp8_Step2.png|thumb|right|300px|State after CMLL: Top corners solved relative to each other, leaving only 8 edges.]]
Once the isolation of the top layer is achieved, the solver uses the [[CMLL]] algorithm set. This step simultaneously orients and permutes the four top corners.

Because the Zeta structure is already stable, the solver can execute these algorithms with high TPS without fear of disturbing the completed slots. Tracking the orientation of the 8 remaining edges during this step is a key advanced technique for a seamless transition to the final phase.

* '''Average Move Count:''' ~12 moves.

== Step 3: 1-Look L8E (Last 8 Edges) ==
[[File:Zeta_Bp8_Step3.png|thumb|right|300px|The goal of Zeta-Bp8: A fully solved cube achieved through a slice-free endgame.]]
The final and most unique phase of Zeta-Bp8 is the '''1-Look L8E'''. This step solves the orientation and permutation of the remaining 8 edges in a single algorithmic sequence.

=== Pure Outer-Layer Ergonomics ===
Zeta-Bp8 explicitly forbids the use of <tt>M, S, or E</tt> slices. The L8E algorithms are optimized for the <tt><U, D, R, L, F, B></tt> move set.
* '''Advantages:''' This prevents mid-solve lockups common in slice-heavy methods and allows for a "gripless" execution style.
* '''Optimization:''' Using software like [[Cube Explorer]], optimal solutions for L8E cases have been found to range between 11 and 15 moves.

'''Example Optimal Generator:'''
<pre>U F R U2 R' F' R' F R B L2 B' U2 (13f*)</pre>

For a full list of all algorithmic cases and execution sheets, see the main [[Zeta-Bp8/L8E Algorithms|Zeta-Bp8 L8E Algorithm Sheet]].

== Pros & Cons ==

{| class="wikitable" style="width:100%;"
! style="background:#d5e8d4; width:50%;" | Pros
! style="background:#f8cecc; width:50%;" | Cons
|-
| valign="top" |
* '''Ergonomic Stability:''' No internal slices in the endgame means zero mechanical lockups.
* '''High Move Efficiency:''' Competes directly with Roux for low move counts (~45 moves).
* '''No EO/EP Pause:''' 1-Look L8E removes the transition pause in the final step.
* '''Total Inspection Freedom:''' Full color neutrality allows for the most efficient blocks possible.
| valign="top" |
* '''F/B Fingertrick Mastery:''' Requires high proficiency with Front and Back face rotations.
* '''Mental Load:''' High demand for lookahead during the Zeta Slotting to CMLL transition.
* '''Algorithm Density:''' 1-Look L8E requires a large number of algorithms to cover all cases without slices.
* '''Intuition Threshold:''' Unconventional blockbuilding has a steeper learning curve than CFOP.
|-
|}

== Performance and Statistics ==
* '''Average Move Count:''' 43-50 moves.
* '''Personal Best (Creator):''' 22.00 seconds.
* '''Ideal Usage:''' Cubers interested in experimental blockbuilding methods and optimizing slice-free endgames.

== See Also ==
* [[Roux]]
* [[CMLL]]
* [[Blockbuilding]]
* [[Method Proposals]]

[[Category:Blockbuilding methods]]

Zeta-Bp8

2026-06-19T19:23:19Z

Hiori Fembysolver:

Zeta-Bp8/L8E Algorithms

2026-06-14T01:07:27Z

Hiori Fembysolver:

<div style="background-color: #fff3cd; border-left: 6px solid #ffc107; padding: 15px; margin-bottom: 25px; border-radius: 4px; color: #856404; font-size: 15px; line-height: 1.5;">
📢 '''Notice:''' Please be advised that our algorithm library will undergo a major update in the near future.
</div>

The '''Zeta-Bp8 L8E Algorithm Sheet''' contains the official slice-free algorithm subsets used in the final stage of the [[Zeta-Bp8]] method. Developed and compiled by '''Hiori (Bernardo Pietro)''', these algorithms are strictly optimized for pure outer-layer ergonomics (<tt><U, D, R, L, F, B></tt>), completely avoiding <tt>M, S, and E</tt> slice turns to prevent mechanical lockups during high-speed execution.

All cases listed below have been verified using optimal solvers, yielding highly efficient solutions ranging from 13 to 15 moves.

== Emergency Rule (Non-Recognition) ==
{| class="wikitable" style="background:#fff9e6; border-left: 5px solid #ffcc00; width:100%; padding:10px;"
| '''Panic/Emergency Rule:''' If you encounter an L8E configuration that you do not recognize or have not memorized yet, '''execute the L8E RouxEo algorithm twice'''. This will safely manipulate the edge states into a predictable orientation or a recognizable pattern without disturbing your completed Zeta blocks.
|}

== 1. Orientation & Core Roux-Style Extensions ==
This subset covers base edge orientation states and transitions derived from standard last-edge profiles, adapted for a slice-free finish.

{| class="wikitable" style="width:100%;"
! style="background:#b3c6ff; width:20%;" | Case Name
! style="background:#b3c6ff; width:65%;" | Algorithm
! style="background:#b3c6ff; width:15%;" | Move Count
|-
| '''L8E RouxEo''' || <tt>U' B' F' D2 F2 R F2 L' B2 F2 R U2 B' F' U2</tt> || 15f*
|-
| '''L8E 2-1L UO''' || <tt>U F R U2 R' F' R' F R B L2 B' U2</tt> || 13f*
|-
| '''L8E F-Front''' || <tt>L2 B F' D' B' L D' B' F L U' B L'</tt> || 13f*
|}

== 2. Arrow & Double Arrow Patterns ==
These cases feature specific "Arrow" shapes formed by misoriented edges on the top and bottom layers.

{| class="wikitable" style="width:100%;"
! style="background:#b3c6ff; width:20%;" | Case Name
! style="background:#b3c6ff; width:65%;" | Algorithm
! style="background:#b3c6ff; width:15%;" | Move Count
|-
| '''L8E I-Arrow''' || <tt>B2 F2 D F2 L R U2 L2 B L R' U' B2 R2 U'</tt> || 15f*
|-
| '''L8E ArrowPermutation''' || <tt>B F' L B' F U' F2 L2 F2 U' R2 B2 R2 U'</tt> || 14f*
|-
| '''L8E Double R-Arrow''' || <tt>U' R2 D' L R' U2 F' D2 U2 B D2 B L' R' U</tt> || 15f*
|}

== 3. S and S2 (Sub-Symmetric) Sets ==
A dense algorithmic subset addressing complex sub-symmetric configurations where multiple pieces require simultaneous orientation and swapping.

{| class="wikitable" style="width:100%;"
! style="background:#b3c6ff; width:20%;" | Case Name
! style="background:#b3c6ff; width:65%;" | Algorithm
! style="background:#b3c6ff; width:15%;" | Move Count
|-
| '''L8E S-0''' || <tt>U2 L' R F' L R U' L R' F R2 B L' R U2</tt> || 15f*
|-
| '''L8E S2-A''' || <tt>B2 F2 D' R' U' R' B' F2 D R D F R' B' U</tt> || 15f*
|-
| '''L8E S2-B''' || <tt>L' R' F' U2 L' R' F2 U L2 F2 L2 D U R2</tt> || 14f*
|-
| '''L8E S2-C''' || <tt>R2 B F D2 R' D2 L U2 B' F L2 D' B2 L2 U'</tt> || 15f*
|-
| '''L8E S2-D''' || <tt>F D2 F2 D2 F2 D' B' R B' F D' B L' B</tt> || 14f*
|-
| '''L8E S2-E''' || <tt>F2 L2 F2 U' B2 U B L' B' R2 D' B' L B' U'</tt> || 15f*
|}

== 4. E Sets & Special Unnamed Variants ==
Advanced endgame permutations characterized by intersecting edge pairs across opposite faces.

{| class="wikitable" style="width:100%;"
! style="background:#b3c6ff; width:20%;" | Case Name
! style="background:#b3c6ff; width:65%;" | Algorithm
! style="background:#b3c6ff; width:15%;" | Move Count
|-
| '''L8E E-A''' || <tt>L R D2 R2 F' D2 B' L2 U2 L' R' U' L2 U'</tt> || 14f*
|-
| '''L8E E-B''' || <tt>F' U' F L' R D' R2 D' U F' D2 U' L R'</tt> || 14f*
|-
| '''L8E Special Var. 1''' || <tt>U' F2 L' R' D2 F D2 F' L' R' B2 R2 U' L2 U2</tt> || 15f*
|-
| '''L8E Special Var. 2''' || <tt>B' F D' U F D U' R B' F D B2 F2 U</tt> || 14f*
|}

== Navigation ==
* Return to the main [[Zeta-Bp8]] documentation page.

[[Category:Algorithm sets]]

Zeta-Bp8

2026-06-11T01:22:53Z

Hiori Fembysolver:

{| class="wikitable" style="float:right; width:280px; margin-left:15px; font-size:95%; border: 1px solid #a2a9b1;"
|-
! colspan="2" style="background:#b3c6ff; text-align:center; font-size:115%; padding:8px;" | Zeta-Bp8 Method
|-
| '''Creator:''' || Bernardo Pietro (Hiori)
|-
| '''Type:''' || Hybrid Blockbuilding / Algorithmic
|-
| '''Steps:''' || 3 (Zeta Slotting, CMLL, 1-Look L8E)
|-
| '''Move Count:''' || 43-50 (Average)
|-
| '''Year:''' || 2026
|-
| '''Key Feature:''' || Pure Outer-Layer Endgame (Slice-Free)
|}

'''Zeta-Bp8''' is an advanced color-neutral 3x3 speedcubing method developed by '''Hiori(Bernardo Pietro)'''. The method is designed to maximize movement efficiency through intuitive blockbuilding while transitioning into a high-TPS, slice-free endgame.

The defining characteristic of Zeta-Bp8 is its total rejection of internal slice moves (M, S, and E) during the final stages of the solve. By utilizing a "Pure Outer-Layer" approach, the method eliminates mechanical lockups and allows solvers to maintain maximum turning speed during the Last 8 Edges (L8E) phase.

== Philosophical Approach ==
Zeta-Bp8 bridges the gap between the intuitive efficiency of [[Roux]] and the algorithmic reliability of [[CFOP]]. It treats the cube not as a series of layers, but as a structure of "Good" and "Bad" edges that dictate the most ergonomic path to completion.

== Step 1: Zeta Slotting ==
[[File:Zeta_Bp8_Step1.png|thumb|right|300px|State after Zeta Slotting: Lower blocks and slots completed, isolating corners and edges.]]
The foundational stage of the method focuses on building the lower structure of the cube using full color neutrality. Instead of a fixed cross, the solver builds blocks and slots dynamically.

=== Edge Classification System ===
The efficiency of this step relies on the solver's ability to classify edges during the 15-second inspection:
* '''Good Edges:''' Edges that can be oriented and solved in 3 moves or less.
* '''Bad Edges:''' Edges that require 4 or more moves to be solved.

The solver manipulates these pieces to ensure the most ergonomic flow, utilizing active lookahead to track corner positions while the final slots are being inserted.

* '''Average Move Count:''' ~18 moves.

== Step 2: CMLL (Corners of the Last Layer) ==
[[File:Zeta_Bp8_Step2.png|thumb|right|300px|State after CMLL: Top corners solved relative to each other, leaving only 8 edges.]]
Once the isolation of the top layer is achieved, the solver uses the [[CMLL]] algorithm set. This step simultaneously orients and permutes the four top corners.

Because the Zeta structure is already stable, the solver can execute these algorithms with high TPS without fear of disturbing the completed slots. Tracking the orientation of the 8 remaining edges during this step is a key advanced technique for a seamless transition to the final phase.

* '''Average Move Count:''' ~12 moves.

== Step 3: 1-Look L8E (Last 8 Edges) ==
[[File:Zeta_Bp8_Step3.png|thumb|right|300px|The goal of Zeta-Bp8: A fully solved cube achieved through a slice-free endgame.]]
The final and most unique phase of Zeta-Bp8 is the '''1-Look L8E'''. This step solves the orientation and permutation of the remaining 8 edges in a single algorithmic sequence.

=== Pure Outer-Layer Ergonomics ===
Zeta-Bp8 explicitly forbids the use of <tt>M, S, or E</tt> slices. The L8E algorithms are optimized for the <tt><U, D, R, L, F, B></tt> move set.
* '''Advantages:''' This prevents mid-solve lockups common in slice-heavy methods and allows for a "gripless" execution style.
* '''Optimization:''' Using software like [[Cube Explorer]], optimal solutions for L8E cases have been found to range between 11 and 15 moves.

'''Example Optimal Generator:'''
<pre>U F R U2 R' F' R' F R B L2 B' U2 (13f*)</pre>

For a full list of all algorithmic cases and execution sheets, see the main [[Zeta-Bp8/L8E Algorithms|Zeta-Bp8 L8E Algorithm Sheet]].

== Pros & Cons ==

{| class="wikitable" style="width:100%;"
! style="background:#d5e8d4; width:50%;" | Pros
! style="background:#f8cecc; width:50%;" | Cons
|-
| valign="top" |
* '''Ergonomic Stability:''' No internal slices in the endgame means zero mechanical lockups.
* '''High Move Efficiency:''' Competes directly with Roux for low move counts (~45 moves).
* '''No EO/EP Pause:''' 1-Look L8E removes the transition pause in the final step.
* '''Total Inspection Freedom:''' Full color neutrality allows for the most efficient blocks possible.
| valign="top" |
* '''F/B Fingertrick Mastery:''' Requires high proficiency with Front and Back face rotations.
* '''Mental Load:''' High demand for lookahead during the Zeta Slotting to CMLL transition.
* '''Algorithm Density:''' 1-Look L8E requires a large number of algorithms to cover all cases without slices.
* '''Intuition Threshold:''' Unconventional blockbuilding has a steeper learning curve than CFOP.
|-
|}

== Performance and Statistics ==
* '''Average Move Count:''' 43-50 moves.
* '''Personal Best (Creator):''' 22.00 seconds.
* '''Ideal Usage:''' Speedcubers looking for a high-TPS alternative to Roux or a more efficient alternative to CFOP.

== See Also ==
* [[Roux]]
* [[CMLL]]
* [[Blockbuilding]]
* [[Method Proposals]]

[[Category:Proposed methods]]
[[Category:Blockbuilding methods]]

Zeta-Bp8/L8E Algorithms

2026-06-11T00:13:21Z

Hiori Fembysolver:

The '''Zeta-Bp8 L8E Algorithm Sheet''' contains the official slice-free algorithm subsets used in the final stage of the [[Zeta-Bp8]] method. Developed and compiled by '''Hiori_Fembysolver''', these algorithms are strictly optimized for pure outer-layer ergonomics (<tt><U, D, R, L, F, B></tt>), completely avoiding <tt>M, S, and E</tt> slice turns to prevent mechanical lockups during high-speed execution.

All cases listed below have been verified using optimal solvers, yielding highly efficient solutions ranging from 13 to 15 moves.

== Emergency Rule (Non-Recognition) ==
{| class="wikitable" style="background:#fff9e6; border-left: 5px solid #ffcc00; width:100%; padding:10px;"
| '''Panic/Emergency Rule:''' If you encounter an L8E configuration that you do not recognize or have not memorized yet, '''execute the L8E RouxEo algorithm twice'''. This will safely manipulate the edge states into a predictable orientation or a recognizable pattern without disturbing your completed Zeta blocks.
|}

== 1. Orientation & Core Roux-Style Extensions ==
This subset covers base edge orientation states and transitions derived from standard last-edge profiles, adapted for a slice-free finish.

{| class="wikitable" style="width:100%;"
! style="background:#b3c6ff; width:20%;" | Case Name
! style="background:#b3c6ff; width:65%;" | Algorithm
! style="background:#b3c6ff; width:15%;" | Move Count
|-
| '''L8E RouxEo''' || <tt>U' B' F' D2 F2 R F2 L' B2 F2 R U2 B' F' U2</tt> || 15f*
|-
| '''L8E 2-1L UO''' || <tt>U F R U2 R' F' R' F R B L2 B' U2</tt> || 13f*
|-
| '''L8E F-Front''' || <tt>L2 B F' D' B' L D' B' F L U' B L'</tt> || 13f*
|}

== 2. Arrow & Double Arrow Patterns ==
These cases feature specific "Arrow" shapes formed by misoriented edges on the top and bottom layers.

{| class="wikitable" style="width:100%;"
! style="background:#b3c6ff; width:20%;" | Case Name
! style="background:#b3c6ff; width:65%;" | Algorithm
! style="background:#b3c6ff; width:15%;" | Move Count
|-
| '''L8E I-Arrow''' || <tt>B2 F2 D F2 L R U2 L2 B L R' U' B2 R2 U'</tt> || 15f*
|-
| '''L8E ArrowPermutation''' || <tt>B F' L B' F U' F2 L2 F2 U' R2 B2 R2 U'</tt> || 14f*
|-
| '''L8E Double R-Arrow''' || <tt>U' R2 D' L R' U2 F' D2 U2 B D2 B L' R' U</tt> || 15f*
|}

== 3. S and S2 (Sub-Symmetric) Sets ==
A dense algorithmic subset addressing complex sub-symmetric configurations where multiple pieces require simultaneous orientation and swapping.

{| class="wikitable" style="width:100%;"
! style="background:#b3c6ff; width:20%;" | Case Name
! style="background:#b3c6ff; width:65%;" | Algorithm
! style="background:#b3c6ff; width:15%;" | Move Count
|-
| '''L8E S-0''' || <tt>U2 L' R F' L R U' L R' F R2 B L' R U2</tt> || 15f*
|-
| '''L8E S2-A''' || <tt>B2 F2 D' R' U' R' B' F2 D R D F R' B' U</tt> || 15f*
|-
| '''L8E S2-B''' || <tt>L' R' F' U2 L' R' F2 U L2 F2 L2 D U R2</tt> || 14f*
|-
| '''L8E S2-C''' || <tt>R2 B F D2 R' D2 L U2 B' F L2 D' B2 L2 U'</tt> || 15f*
|-
| '''L8E S2-D''' || <tt>F D2 F2 D2 F2 D' B' R B' F D' B L' B</tt> || 14f*
|-
| '''L8E S2-E''' || <tt>F2 L2 F2 U' B2 U B L' B' R2 D' B' L B' U'</tt> || 15f*
|}

== 4. E Sets & Special Unnamed Variants ==
Advanced endgame permutations characterized by intersecting edge pairs across opposite faces.

{| class="wikitable" style="width:100%;"
! style="background:#b3c6ff; width:20%;" | Case Name
! style="background:#b3c6ff; width:65%;" | Algorithm
! style="background:#b3c6ff; width:15%;" | Move Count
|-
| '''L8E E-A''' || <tt>L R D2 R2 F' D2 B' L2 U2 L' R' U' L2 U'</tt> || 14f*
|-
| '''L8E E-B''' || <tt>F' U' F L' R D' R2 D' U F' D2 U' L R'</tt> || 14f*
|-
| '''L8E Special Var. 1''' || <tt>U' F2 L' R' D2 F D2 F' L' R' B2 R2 U' L2 U2</tt> || 15f*
|-
| '''L8E Special Var. 2''' || <tt>B' F D' U F D U' R B' F D B2 F2 U</tt> || 14f*
|}

== Navigation ==
* Return to the main [[Zeta-Bp8]] documentation page.

[[Category:Algorithm sets]]

Zeta-Bp8

2026-06-11T00:11:01Z

Hiori Fembysolver:

{| class="wikitable" style="float:right; width:280px; margin-left:15px; font-size:95%; border: 1px solid #a2a9b1;"
|-
! colspan="2" style="background:#b3c6ff; text-align:center; font-size:115%; padding:8px;" | Zeta-Bp8 Method
|-
| '''Creator:''' || Bernardo Pietro (Hiori)
|-
| '''Type:''' || Hybrid Blockbuilding / Algorithmic
|-
| '''Steps:''' || 3 (Zeta Slotting, CMLL, 1-Look L8E)
|-
| '''Move Count:''' || 43-50 (Average)
|-
| '''Year:''' || 2026
|-
| '''Key Feature:''' || Pure Outer-Layer Endgame (Slice-Free)
|}

'''Zeta-Bp8''' is an advanced color-neutral 3x3 speedcubing method developed by '''Hiori_Fembysolver'''. The method is designed to maximize movement efficiency through intuitive blockbuilding while transitioning into a high-TPS, slice-free endgame.

The defining characteristic of Zeta-Bp8 is its total rejection of internal slice moves (M, S, and E) during the final stages of the solve. By utilizing a "Pure Outer-Layer" approach, the method eliminates mechanical lockups and allows solvers to maintain maximum turning speed during the Last 8 Edges (L8E) phase.

== Philosophical Approach ==
Zeta-Bp8 bridges the gap between the intuitive efficiency of [[Roux]] and the algorithmic reliability of [[CFOP]]. It treats the cube not as a series of layers, but as a structure of "Good" and "Bad" edges that dictate the most ergonomic path to completion.

== Step 1: Zeta Slotting ==
[[File:Zeta_Bp8_Step1.png|thumb|right|300px|State after Zeta Slotting: Lower blocks and slots completed, isolating corners and edges.]]
The foundational stage of the method focuses on building the lower structure of the cube using full color neutrality. Instead of a fixed cross, the solver builds blocks and slots dynamically.

=== Edge Classification System ===
The efficiency of this step relies on the solver's ability to classify edges during the 15-second inspection:
* '''Good Edges:''' Edges that can be oriented and solved in 3 moves or less.
* '''Bad Edges:''' Edges that require 4 or more moves to be solved.

The solver manipulates these pieces to ensure the most ergonomic flow, utilizing active lookahead to track corner positions while the final slots are being inserted.

* '''Average Move Count:''' ~18 moves.

== Step 2: CMLL (Corners of the Last Layer) ==
[[File:Zeta_Bp8_Step2.png|thumb|right|300px|State after CMLL: Top corners solved relative to each other, leaving only 8 edges.]]
Once the isolation of the top layer is achieved, the solver uses the [[CMLL]] algorithm set. This step simultaneously orients and permutes the four top corners.

Because the Zeta structure is already stable, the solver can execute these algorithms with high TPS without fear of disturbing the completed slots. Tracking the orientation of the 8 remaining edges during this step is a key advanced technique for a seamless transition to the final phase.

* '''Average Move Count:''' ~12 moves.

== Step 3: 1-Look L8E (Last 8 Edges) ==
[[File:Zeta_Bp8_Step3.png|thumb|right|300px|The goal of Zeta-Bp8: A fully solved cube achieved through a slice-free endgame.]]
The final and most unique phase of Zeta-Bp8 is the '''1-Look L8E'''. This step solves the orientation and permutation of the remaining 8 edges in a single algorithmic sequence.

=== Pure Outer-Layer Ergonomics ===
Zeta-Bp8 explicitly forbids the use of <tt>M, S, or E</tt> slices. The L8E algorithms are optimized for the <tt><U, D, R, L, F, B></tt> move set.
* '''Advantages:''' This prevents mid-solve lockups common in slice-heavy methods and allows for a "gripless" execution style.
* '''Optimization:''' Using software like [[Cube Explorer]], optimal solutions for L8E cases have been found to range between 11 and 15 moves.

'''Example Optimal Generator:'''
<pre>U F R U2 R' F' R' F R B L2 B' U2 (13f*)</pre>

For a full list of all algorithmic cases and execution sheets, see the main [[Zeta-Bp8/L8E Algorithms|Zeta-Bp8 L8E Algorithm Sheet]].

== Pros & Cons ==

{| class="wikitable" style="width:100%;"
! style="background:#d5e8d4; width:50%;" | Pros
! style="background:#f8cecc; width:50%;" | Cons
|-
| valign="top" |
* '''Ergonomic Stability:''' No internal slices in the endgame means zero mechanical lockups.
* '''High Move Efficiency:''' Competes directly with Roux for low move counts (~45 moves).
* '''No EO/EP Pause:''' 1-Look L8E removes the transition pause in the final step.
* '''Total Inspection Freedom:''' Full color neutrality allows for the most efficient blocks possible.
| valign="top" |
* '''F/B Fingertrick Mastery:''' Requires high proficiency with Front and Back face rotations.
* '''Mental Load:''' High demand for lookahead during the Zeta Slotting to CMLL transition.
* '''Algorithm Density:''' 1-Look L8E requires a large number of algorithms to cover all cases without slices.
* '''Intuition Threshold:''' Unconventional blockbuilding has a steeper learning curve than CFOP.
|-
|}

== Performance and Statistics ==
* '''Average Move Count:''' 43-50 moves.
* '''Personal Best (Creator):''' 22.00 seconds.
* '''Ideal Usage:''' Speedcubers looking for a high-TPS alternative to Roux or a more efficient alternative to CFOP.

== See Also ==
* [[Roux]]
* [[CMLL]]
* [[Blockbuilding]]
* [[Method Proposals]]

[[Category:Proposed methods]]
[[Category:Blockbuilding methods]]

Zeta-Bp8/L8E Algorithms

2026-06-11T00:09:14Z

Hiori Fembysolver: Creating L8E algorithm subpage

The '''Zeta-Bp8 L8E Algorithm Sheet''' contains the official slice-free algorithm subsets used in the final stage of the [[Zeta-Bp8]] method. Developed and compiled by '''Hiori_Fembysolver''', these algorithms are strictly optimized for pure outer-layer ergonomics (<tt><U, D, R, L, F, B></tt>), completely avoiding <tt>M, S, and E</tt> slice turns to prevent mechanical lockups during high-speed execution.

All cases listed below have been verified using optimal solvers, yielding highly efficient solutions ranging from 13 to 15 moves.

== 1. Orientation & Core Roux-Style Extensions ==
This subset covers base edge orientation states and transitions derived from standard last-edge profiles, adapted for a slice-free finish.

{| class="wikitable" style="width:100%;"
! style="background:#b3c6ff; width:20%;" | Case Name
! style="background:#b3c6ff; width:65%;" | Algorithm
! style="background:#b3c6ff; width:15%;" | Move Count
|-
| '''L8E RouxEo''' || <tt>U' B' F' D2 F2 R F2 L' B2 F2 R U2 B' F' U2</tt> || 15f*
|-
| '''L8E 2-1L UO''' || <tt>U F R U2 R' F' R' F R B L2 B' U2</tt> || 13f*
|-
| '''L8E F-Front''' || <tt>L2 B F' D' B' L D' B' F L U' B L'</tt> || 13f*
|}

== 2. Arrow & Double Arrow Patterns ==
These cases feature specific "Arrow" shapes formed by misoriented edges on the top and bottom layers.

{| class="wikitable" style="width:100%;"
! style="background:#b3c6ff; width:20%;" | Case Name
! style="background:#b3c6ff; width:65%;" | Algorithm
! style="background:#b3c6ff; width:15%;" | Move Count
|-
| '''L8E I-Arrow''' || <tt>B2 F2 D F2 L R U2 L2 B L R' U' B2 R2 U'</tt> || 15f*
|-
| '''L8E ArrowPermutation''' || <tt>B F' L B' F U' F2 L2 F2 U' R2 B2 R2 U'</tt> || 14f*
|-
| '''L8E Double R-Arrow''' || <tt>U' R2 D' L R' U2 F' D2 U2 B D2 B L' R' U</tt> || 15f*
|}

== 3. S and S2 (Sub-Symmetric) Sets ==
A dense algorithmic subset addressing complex sub-symmetric configurations where multiple pieces require simultaneous orientation and swapping.

{| class="wikitable" style="width:100%;"
! style="background:#b3c6ff; width:20%;" | Case Name
! style="background:#b3c6ff; width:65%;" | Algorithm
! style="background:#b3c6ff; width:15%;" | Move Count
|-
| '''L8E S-0''' || <tt>U2 L' R F' L R U' L R' F R2 B L' R U2</tt> || 15f*
|-
| '''L8E S2-A''' || <tt>B2 F2 D' R' U' R' B' F2 D R D F R' B' U</tt> || 15f*
|-
| '''L8E S2-B''' || <tt>L' R' F' U2 L' R' F2 U L2 F2 L2 D U R2</tt> || 14f*
|-
| '''L8E S2-C''' || <tt>R2 B F D2 R' D2 L U2 B' F L2 D' B2 L2 U'</tt> || 15f*
|-
| '''L8E S2-D''' || <tt>F D2 F2 D2 F2 D' B' R B' F D' B L' B</tt> || 14f*
|-
| '''L8E S2-E''' || <tt>F2 L2 F2 U' B2 U B L' B' R2 D' B' L B' U'</tt> || 15f*
|}

== 4. E Sets & Special Unnamed Variants ==
Advanced endgame permutations characterized by intersecting edge pairs across opposite faces.

{| class="wikitable" style="width:100%;"
! style="background:#b3c6ff; width:20%;" | Case Name
! style="background:#b3c6ff; width:65%;" | Algorithm
! style="background:#b3c6ff; width:15%;" | Move Count
|-
| '''L8E E-A''' || <tt>L R D2 R2 F' D2 B' L2 U2 L' R' U' L2 U'</tt> || 14f*
|-
| '''L8E E-B''' || <tt>F' U' F L' R D' R2 D' U F' D2 U' L R'</tt> || 14f*
|-
| '''L8E Special Var. 1''' || <tt>U' F2 L' R' D2 F D2 F' L' R' B2 R2 U' L2 U2</tt> ||

Zeta-Bp8

2026-06-11T00:07:26Z

Hiori Fembysolver: /* Step 3: 1-Look L8E (Last 8 Edges) */

{| class="wikitable" style="float:right; width:280px; margin-left:15px; font-size:95%; border: 1px solid #a2a9b1;"
|-
! colspan="2" style="background:#b3c6ff; text-align:center; font-size:115%; padding:8px;" | Zeta-Bp8 Method
|-
| '''Creator:''' || Hiori_Fembysolver
|-
| '''Type:''' || Hybrid Blockbuilding / Algorithmic
|-
| '''Steps:''' || 3 (Zeta Slotting, CMLL, 1-Look L8E)
|-
| '''Move Count:''' || 43-50 (Average)
|-
| '''Year:''' || 2026
|-
| '''Key Feature:''' || Pure Outer-Layer Endgame (Slice-Free)
|}

'''Zeta-Bp8''' is an advanced color-neutral 3x3 speedcubing method developed by '''Hiori_Fembysolver'''. The method is designed to maximize movement efficiency through intuitive blockbuilding while transitioning into a high-TPS, slice-free endgame.

The defining characteristic of Zeta-Bp8 is its total rejection of internal slice moves (M, S, and E) during the final stages of the solve. By utilizing a "Pure Outer-Layer" approach, the method eliminates mechanical lockups and allows solvers to maintain maximum turning speed during the Last 8 Edges (L8E) phase.

== Philosophical Approach ==
Zeta-Bp8 bridges the gap between the intuitive efficiency of [[Roux]] and the algorithmic reliability of [[CFOP]]. It treats the cube not as a series of layers, but as a structure of "Good" and "Bad" edges that dictate the most ergonomic path to completion.

== Step 1: Zeta Slotting ==
[[File:Zeta_Bp8_Step1.png|thumb|right|300px|State after Zeta Slotting: Lower blocks and slots completed, isolating corners and edges.]]
The foundational stage of the method focuses on building the lower structure of the cube using full color neutrality. Instead of a fixed cross, the solver builds blocks and slots dynamically.

=== Edge Classification System ===
The efficiency of this step relies on the solver's ability to classify edges during the 15-second inspection:
* '''Good Edges:''' Edges that can be oriented and solved in 3 moves or less.
* '''Bad Edges:''' Edges that require 4 or more moves to be solved.

The solver manipulates these pieces to ensure the most ergonomic flow, utilizing active lookahead to track corner positions while the final slots are being inserted.

* '''Average Move Count:''' ~18 moves.

== Step 2: CMLL (Corners of the Last Layer) ==
[[File:Zeta_Bp8_Step2.png|thumb|right|300px|State after CMLL: Top corners solved relative to each other, leaving only 8 edges.]]
Once the isolation of the top layer is achieved, the solver uses the [[CMLL]] algorithm set. This step simultaneously orients and permutes the four top corners.

Because the Zeta structure is already stable, the solver can execute these algorithms with high TPS without fear of disturbing the completed slots. Tracking the orientation of the 8 remaining edges during this step is a key advanced technique for a seamless transition to the final phase.

* '''Average Move Count:''' ~12 moves.

== Step 3: 1-Look L8E (Last 8 Edges) ==
[[File:Zeta_Bp8_Step3.png|thumb|right|300px|The goal of Zeta-Bp8: A fully solved cube achieved through a slice-free endgame.]]
The final and most unique phase of Zeta-Bp8 is the '''1-Look L8E'''. This step solves the orientation and permutation of the remaining 8 edges in a single algorithmic sequence.

=== Pure Outer-Layer Ergonomics ===
Zeta-Bp8 explicitly forbids the use of <tt>M, S, or E</tt> slices. The L8E algorithms are optimized for the <tt><U, D, R, L, F, B></tt> move set.
* '''Advantages:''' This prevents mid-solve lockups common in slice-heavy methods and allows for a "gripless" execution style.
* '''Optimization:''' Using software like [[Cube Explorer]], optimal solutions for L8E cases have been found to range between 11 and 15 moves.

'''Example Optimal Generator:'''
<pre>U F R U2 R' F' R' F R B L2 B' U2 (13f*)</pre>

For a full list of all algorithmic cases and execution sheets, see the main [[Zeta-Bp8/L8E Algorithms|Zeta-Bp8 L8E Algorithm Sheet]].

== Pros & Cons ==

{| class="wikitable" style="width:100%;"
! style="background:#d5e8d4; width:50%;" | Pros
! style="background:#f8cecc; width:50%;" | Cons
|-
| valign="top" |
* '''Ergonomic Stability:''' No internal slices in the endgame means zero mechanical lockups.
* '''High Move Efficiency:''' Competes directly with Roux for low move counts (~45 moves).
* '''No EO/EP Pause:''' 1-Look L8E removes the transition pause in the final step.
* '''Total Inspection Freedom:''' Full color neutrality allows for the most efficient blocks possible.
| valign="top" |
* '''F/B Fingertrick Mastery:''' Requires high proficiency with Front and Back face rotations.
* '''Mental Load:''' High demand for lookahead during the Zeta Slotting to CMLL transition.
* '''Algorithm Density:''' 1-Look L8E requires a large number of algorithms to cover all cases without slices.
* '''Intuition Threshold:''' Unconventional blockbuilding has a steeper learning curve than CFOP.
|-
|}

== Performance and Statistics ==
* '''Average Move Count:''' 43-50 moves.
* '''Personal Best (Creator):''' 22.00 seconds.
* '''Ideal Usage:''' Speedcubers looking for a high-TPS alternative to Roux or a more efficient alternative to CFOP.

== See Also ==
* [[Roux]]
* [[CMLL]]
* [[Blockbuilding]]
* [[Method Proposals]]

[[Category:Proposed methods]]
[[Category:Blockbuilding methods]]

Zeta-Bp8

2026-06-11T00:01:20Z

Hiori Fembysolver:

{| class="wikitable" style="float:right; width:280px; margin-left:15px; font-size:95%; border: 1px solid #a2a9b1;"
|-
! colspan="2" style="background:#b3c6ff; text-align:center; font-size:115%; padding:8px;" | Zeta-Bp8 Method
|-
| '''Creator:''' || Hiori_Fembysolver
|-
| '''Type:''' || Hybrid Blockbuilding / Algorithmic
|-
| '''Steps:''' || 3 (Zeta Slotting, CMLL, 1-Look L8E)
|-
| '''Move Count:''' || 43-50 (Average)
|-
| '''Year:''' || 2026
|-
| '''Key Feature:''' || Pure Outer-Layer Endgame (Slice-Free)
|}

'''Zeta-Bp8''' is an advanced color-neutral 3x3 speedcubing method developed by '''Hiori_Fembysolver'''. The method is designed to maximize movement efficiency through intuitive blockbuilding while transitioning into a high-TPS, slice-free endgame.

The defining characteristic of Zeta-Bp8 is its total rejection of internal slice moves (M, S, and E) during the final stages of the solve. By utilizing a "Pure Outer-Layer" approach, the method eliminates mechanical lockups and allows solvers to maintain maximum turning speed during the Last 8 Edges (L8E) phase.

== Philosophical Approach ==
Zeta-Bp8 bridges the gap between the intuitive efficiency of [[Roux]] and the algorithmic reliability of [[CFOP]]. It treats the cube not as a series of layers, but as a structure of "Good" and "Bad" edges that dictate the most ergonomic path to completion.

== Step 1: Zeta Slotting ==
[[File:Zeta_Bp8_Step1.png|thumb|right|300px|State after Zeta Slotting: Lower blocks and slots completed, isolating corners and edges.]]
The foundational stage of the method focuses on building the lower structure of the cube using full color neutrality. Instead of a fixed cross, the solver builds blocks and slots dynamically.

=== Edge Classification System ===
The efficiency of this step relies on the solver's ability to classify edges during the 15-second inspection:
* '''Good Edges:''' Edges that can be oriented and solved in 3 moves or less.
* '''Bad Edges:''' Edges that require 4 or more moves to be solved.

The solver manipulates these pieces to ensure the most ergonomic flow, utilizing active lookahead to track corner positions while the final slots are being inserted.

* '''Average Move Count:''' ~18 moves.

== Step 2: CMLL (Corners of the Last Layer) ==
[[File:Zeta_Bp8_Step2.png|thumb|right|300px|State after CMLL: Top corners solved relative to each other, leaving only 8 edges.]]
Once the isolation of the top layer is achieved, the solver uses the [[CMLL]] algorithm set. This step simultaneously orients and permutes the four top corners.

Because the Zeta structure is already stable, the solver can execute these algorithms with high TPS without fear of disturbing the completed slots. Tracking the orientation of the 8 remaining edges during this step is a key advanced technique for a seamless transition to the final phase.

* '''Average Move Count:''' ~12 moves.

== Step 3: 1-Look L8E (Last 8 Edges) ==
[[File:Zeta_Bp8_Step3.png|thumb|right|300px|The goal of Zeta-Bp8: A fully solved cube achieved through a slice-free endgame.]]
The final and most unique phase of Zeta-Bp8 is the '''1-Look L8E'''. This step solves the orientation and permutation of the remaining 8 edges in a single algorithmic sequence.

=== Pure Outer-Layer Ergonomics ===
Zeta-Bp8 explicitly forbids the use of <tt>M, S, or E</tt> slices. The L8E algorithms are optimized for the <tt><U, D, R, L, F, B></tt> move set.
* '''Advantages:''' This prevents mid-solve lockups common in slice-heavy methods and allows for a "gripless" execution style.
* '''Optimization:''' Using software like [[Cube Explorer]], optimal solutions for L8E cases have been found to range between 11 and 15 moves.

'''Example Optimal Generator:'''
<pre>U F R U2 R' F' R' F R B L2 B' U2 (13f*)</pre>

== Pros & Cons ==

{| class="wikitable" style="width:100%;"
! style="background:#d5e8d4; width:50%;" | Pros
! style="background:#f8cecc; width:50%;" | Cons
|-
| valign="top" |
* '''Ergonomic Stability:''' No internal slices in the endgame means zero mechanical lockups.
* '''High Move Efficiency:''' Competes directly with Roux for low move counts (~45 moves).
* '''No EO/EP Pause:''' 1-Look L8E removes the transition pause in the final step.
* '''Total Inspection Freedom:''' Full color neutrality allows for the most efficient blocks possible.
| valign="top" |
* '''F/B Fingertrick Mastery:''' Requires high proficiency with Front and Back face rotations.
* '''Mental Load:''' High demand for lookahead during the Zeta Slotting to CMLL transition.
* '''Algorithm Density:''' 1-Look L8E requires a large number of algorithms to cover all cases without slices.
* '''Intuition Threshold:''' Unconventional blockbuilding has a steeper learning curve than CFOP.
|-
|}

== Performance and Statistics ==
* '''Average Move Count:''' 43-50 moves.
* '''Personal Best (Creator):''' 22.00 seconds.
* '''Ideal Usage:''' Speedcubers looking for a high-TPS alternative to Roux or a more efficient alternative to CFOP.

== See Also ==
* [[Roux]]
* [[CMLL]]
* [[Blockbuilding]]
* [[Method Proposals]]

[[Category:Proposed methods]]
[[Category:Blockbuilding methods]]

Zeta-Bp8

2026-06-11T00:00:41Z

Hiori Fembysolver:

{| class="wikitable" style="float:right; width:280px; margin-left:15px; font-size:95%; border: 1px solid #a2a9b1;"
|-
! colspan="2" style="background:#b3c6ff; text-align:center; font-size:115%; padding:8px;" | Zeta-Bp8 Method
|-
| '''Creator:''' || Hiori_Fembysolver
|-
| '''Type:''' || Hybrid Blockbuilding / Algorithmic
|-
| '''Steps:''' || 3 (Zeta Slotting, CMLL, 1-Look L8E)
|-
| '''Move Count:''' || 43-50 (Average)
|-
| '''Year:''' || 2026
|-
| '''Key Feature:''' || Pure Outer-Layer Endgame (Slice-Free)
|}

'''Zeta-Bp8''' is an advanced color-neutral 3x3 speedcubing method developed by '''Hiori_Fembysolver'''. The method is designed to maximize movement efficiency through intuitive blockbuilding while transitioning into a high-TPS, slice-free endgame.

The defining characteristic of Zeta-Bp8 is its total rejection of internal slice moves (M, S, and E) during the final stages of the solve. By utilizing a "Pure Outer-Layer" approach, the method eliminates mechanical lockups and allows solvers to maintain maximum turning speed during the Last 8 Edges (L8E) phase.

== Philosophical Approach ==
Zeta-Bp8 bridges the gap between the intuitive efficiency of [[Roux]] and the algorithmic reliability of [[CFOP]]. It treats the cube not as a series of layers, but as a structure of "Good" and "Bad"
=== Edge Classification System ===
The efficiency of this step relies on the solver's ability to classify edges during the 15-second inspection:
* '''Good Edges:''' Edges that can be oriented and solved in 3 moves or less.
* '''Bad Edges:''' Edges that require 4 or more moves to be solved.

The solver manipulates these pieces to ensure the most ergonomic flow, utilizing active lookahead to track corner positions while the final slots are being inserted.

* '''Average Move Count:''' ~18 moves.

== Step 2: CMLL (Corners of the Last Layer) ==
[[File:Zeta_cmll_state.png|thumb|right|300px|State after CMLL: Top corners solved relative to each other, leaving only 8 edges.]]
Once the isolation of the top layer is achieved, the solver uses the [[CMLL]] algorithm set. This step simultaneously orients and permutes the four top corners.

Because the Zeta structure is already stable, the solver can execute these algorithms with high TPS without fear of disturbing the completed slots. Tracking the orientation of the 8 remaining edges during this step is a key advanced technique for a seamless transition to the final phase.

* '''Average Move Count:''' ~12 moves.

== Step 3: 1-Look L8E (Last 8 Edges) ==
[[File:Zeta_solved_state.png|thumb|right|300px|The goal of Zeta-Bp8: A fully solved cube achieved through a slice-free endgame.]]
The final and most unique phase of Zeta-Bp8 is the '''1-Look L8E'''. This step solves the orientation and permutation of the remaining 8 edges in a single algorithmic sequence.

=== Pure Outer-Layer Ergonomics ===
Zeta-Bp8 explicitly forbids the use of <tt>M, S, or E</tt> slices. The L8E algorithms are optimized for the <tt><U, D, R, L, F, B></tt> move set.
* '''Advantages:''' This prevents mid-solve lockups common in slice-heavy methods and allows for a "gripless" execution style.
* '''Optimization:''' Using software like [[Cube Explorer]], optimal solutions for L8E cases have been found to range between 11 and 15 moves.

'''Example Optimal Generator:'''
<pre>U F R U2 R' F' R' F R B L2 B' U2 (13f*)</pre>

== Pros & Cons ==

{| class="wikitable" style="width:100%;"
! style="background:#d5e8d4; width:50%;" | Pros
! style="background:#f8cecc; width:50%;" | Cons
|-
| valign="top" |
* '''Ergonomic Stability:''' No internal slices in the endgame means zero mechanical lockups.
* '''High Move Efficiency:''' Competes directly with Roux for low move counts (~45 moves).
* '''No EO/EP Pause:''' 1-Look L8E removes the transition pause in the final step.
* '''Total Inspection Freedom:''' Full color neutrality allows for the most efficient blocks possible.
| valign="top" |
* '''F/B Fingertrick Mastery:''' Requires high proficiency with Front and Back face rotations.
* '''Mental Load:''' High demand for lookahead during the Zeta Slotting to CMLL transition.
* '''Algorithm Density:''' 1-Look L8E requires a large number of algorithms to cover all cases without slices.
* '''Intuition Threshold:''' Unconventional blockbuilding has a steeper learning curve than CFOP.
|-
|}

== Performance and Statistics ==
* '''Average Move Count:''' 43-50 moves.
* '''Personal Best (Creator):''' 22.00 seconds.
* '''Ideal Usage:''' Speedcubers looking for a high-TPS alternative to Roux or a more efficient alternative to CFOP.

== See Also ==
* [[Roux]]
* [[CMLL]]
* [[Blockbuilding]]
* [[Method Proposals]]

[[Category:Proposed methods]]
[[Category:Blockbuilding methods]]

Zeta-Bp8

2026-06-10T23:59:55Z

Hiori Fembysolver:

Zeta-Bp8

2026-06-10T23:58:26Z

Hiori Fembysolver:

{| class="wikitable" style="float:right; width:280px; margin-left:15px; font-size:95%; border: 1px solid #a2a9b1;"
|-
! colspan="2" style="background:#b3c6ff; text-align:center; font-size:115%; padding:8px;" | Zeta-Bp8 Method
|-
| '''Creator:''' || Hiori_Fembysolver
|-
| '''Type:''' || Hybrid Blockbuilding / Algorithmic
|-
| '''Steps:''' || 3 (Zeta Slotting, CMLL, 1-Look L8E)
|-
| '''Move Count:''' || 43-50 (Average)
|-
| '''Year:''' || 2026
|-
| '''Key Feature:''' || Pure Outer-Layer Endgame (Slice-Free)
|}

'''Zeta-Bp8''' is an advanced color-neutral 3x3 speedcubing method developed by '''Hiori_Fembysolver'''. The method is designed to maximize movement efficiency through intuitive blockbuilding while transitioning into a high-TPS, slice-free endgame.

The defining characteristic of Zeta-Bp8 is its total rejection of internal slice moves (M, S, and E) during the final stages of the solve. By utilizing a "Pure Outer-Layer" approach, the method eliminates mechanical lockups and allows solvers to maintain maximum turning speed during the Last 8 Edges (L8E) phase.

== Philosophical Approach ==
Zeta-Bp8 bridges the gap between the intuitive efficiency of [[Roux]] and the algorithmic reliability of [[CFOP]]. It treats the cube not as a series of layers, but as a structure of "Good" and "Bad" edges that dictate the most ergonomic path to completion.

== Step 1: Zeta Slotting ==
[[File:Zeta_slotting_state.png|thumb|right|300px|State after Zeta Slotting: Lower blocks and slots completed, isolating corners and edges.]]
The foundational stage of the method focuses on building the lower structure of the cube using full color neutrality. Instead of a fixed cross, the solver builds blocks and slots dynamically.

=== Edge Classification System ===
The efficiency of this step relies on the solver's ability to classify edges during the 15-second inspection:
* '''Good Edges:''' Edges that can be oriented and solved in 3 moves or less.
* '''Bad Edges:''' Edges that require 4 or more moves to be solved.

The solver manipulates these pieces to ensure the most ergonomic flow, utilizing active lookahead to track corner positions while the final slots are being inserted.

* '''Average Move Count:''' ~18 moves.

== Step 2: CMLL (Corners of the Last Layer) ==
[[File:Zeta_cmll_state.png|thumb|right|300px|State after CMLL: Top corners solved relative to each other, leaving only 8 edges.]]
Once the isolation of the top layer is achieved, the solver uses the [[CMLL]] algorithm set. This step simultaneously orients and permutes the four top corners.

Because the Zeta structure is already stable, the solver can execute these algorithms with high TPS without fear of disturbing the completed slots. Tracking the orientation of the 8 remaining edges during this step is a key advanced technique for a seamless transition to the final phase.

* '''Average Move Count:''' ~12 moves.

== Step 3: 1-Look L8E (Last 8 Edges) ==
[[File:Zeta_solved_state.png|thumb|right|300px|The goal of Zeta-Bp8: A fully solved cube achieved through a slice-free endgame.]]
The final and most unique phase of Zeta-Bp8 is the '''1-Look L8E'''. This step solves the orientation and permutation of the remaining 8 edges in a single algorithmic sequence.

=== Pure Outer-Layer Ergonomics ===
Zeta-Bp8 explicitly forbids the use of <tt>M, S, or E</tt> slices. The L8E algorithms are optimized for the <tt><U, D, R, L, F, B></tt> move set.
* '''Advantages:''' This prevents mid-solve lockups common in slice-heavy methods and allows for a "gripless" execution style.
* '''Optimization:''' Using software like [[Cube Explorer]], optimal solutions for L8E cases have been found to range between 11 and 15 moves.

'''Example Optimal Generator:'''
<pre>U F R U2 R' F' R' F R B L2 B' U2 (13f*)</pre>

== Pros & Cons ==

{| class="wikitable" style="width:100%;"
! style="background:#d5e8d4; width:50%;" | Pros
! style="background:#f8cecc; width:50%;" | Cons
|-
| valign="top" |
* '''Ergonomic Stability:''' No internal slices in the endgame means zero mechanical lockups.
* '''High Move Efficiency:''' Competes directly with Roux for low move counts (~45 moves).
* '''No EO/EP Pause:''' 1-Look L8E removes the transition pause in the final step.
* '''Total Inspection Freedom:''' Full color neutrality allows for the most efficient blocks possible.
| valign="top" |
* '''F/B Fingertrick Mastery:''' Requires high proficiency with Front and Back face rotations.
* '''Mental Load:''' High demand for lookahead during the Zeta Slotting to CMLL transition.
* '''Algorithm Density:''' 1-Look L8E requires a large number of algorithms to cover all cases without slices.
* '''Intuition Threshold:''' Unconventional blockbuilding has a steeper learning curve than CFOP.
|-
|}

== Performance and Statistics ==
* '''Average Move Count:''' 43-50 moves.
* '''Personal Best (Creator):''' 22.00 seconds.
* '''Ideal Usage:''' Speedcubers looking for a high-TPS alternative to Roux or a more efficient alternative to CFOP.

== See Also ==
* [[Roux]]
* [[CMLL]]
* [[Blockbuilding]]
* [[Method Proposals]]

[[Category:Proposed methods]]
[[Category:Blockbuilding methods]]

File:Zeta Bp8 Step3.png

2026-06-10T23:55:33Z

Hiori Fembysolver:

File:Zeta Bp8 Step2.png

2026-06-10T23:54:41Z

Hiori Fembysolver:

File:Zeta Bp8 Step1.png

2026-06-10T23:52:48Z

Hiori Fembysolver:

Zeta-Bp8

2026-06-10T23:52:21Z

Hiori Fembysolver: Initial page creation for Zeta-Bp8 method

{{Infobox method
| name = Zeta-Bp8
| creator = Hiori_Fembysolver
| type = Hybrid Blockbuilding / Algorithmic
| steps = 3 (Zeta Slotting, CMLL, 1-Look L8E)
| movecount = 43-50 (Average)
| postdate = 2026
| variants = Zeta-Bp8 Pure Outer-Layer
}}

'''Zeta-Bp8''' is an advanced color-neutral 3x3 speedcubing method developed by '''Hiori_Fembysolver'''. The method is designed to maximize movement efficiency through intuitive blockbuilding while transitioning into a high-TPS, slice-free endgame.

The defining characteristic of Zeta-Bp8 is its total rejection of internal slice moves (M, S, and E) during the final stages of the solve. By utilizing a "Pure Outer-Layer" approach, the method eliminates mechanical lockups and allows solvers to maintain maximum turning speed during the Last 8 Edges (L8E) phase.

== Philosophical Approach ==
Zeta-Bp8 bridges the gap between the intuitive efficiency of [[Roux]] and the algorithmic reliability of [[CFOP]]. It treats the cube not as a series of layers, but as a structure of "Good" and "Bad" edges that dictate the most ergonomic path to completion.

== Step 1: Zeta Slotting ==
[[File:Zeta_Bp8_Step1.png|thumb|right|300px|State after Zeta Slotting: Lower blocks and slots completed, isolating corners and edges.]]
The foundational stage of the method focuses on building the lower structure of the cube using full color neutrality. Instead of a fixed cross, the solver builds blocks and slots dynamically.

=== Edge Classification System ===
The efficiency of this step relies on the solver's ability to classify edges during the 15-second inspection:
* '''Good Edges:''' Edges that can be oriented and solved in 3 moves or less.
* '''Bad Edges:''' Edges that require 4 or more moves to be solved.

The solver manipulates these pieces to ensure the most ergonomic flow, utilizing active lookahead to track corner positions while the final slots are being inserted.

* '''Average Move Count:''' 18 moves.

== Step 2: CMLL (Corners of the Last Layer) ==
[[File:Zeta_Bp8_Step2.png|thumb|right|300px|State after CMLL: Top corners solved relative to each other, leaving only 8 edges.]]
Once the isolation of the top layer is achieved, the solver uses the [[CMLL]] algorithm set. This step simultaneously orients and permutes the four top corners.

Because the Zeta structure is already stable, the solver can execute these algorithms with high TPS without fear of disturbing the completed slots. Tracking the orientation of the 8 remaining edges during this step is a key advanced technique for a seamless transition to the final phase.

* '''Average Move Count:''' 12 moves.

== Step 3: 1-Look L8E (Last 8 Edges) ==
[[File:Zeta_Bp8_Step3.png|thumb|right|300px|The goal of Zeta-Bp8: A fully solved cube achieved through a slice-free endgame.]]
The final and most unique phase of Zeta-Bp8 is the '''1-Look L8E'''. This step solves the orientation and permutation of the remaining 8 edges in a single algorithmic sequence.

=== Pure Outer-Layer Ergonomics ===
Zeta-Bp8 explicitly forbids the use of <tt>M, S, or E</tt> slices. The L8E algorithms are optimized for the <tt><U, D, R, L, F, B></tt> move set.
* '''Advantages:''' This prevents mid-solve lockups common in slice-heavy methods and allows for a "gripless" execution style.
* '''Optimization:''' Using software like [[Cube Explorer]], optimal solutions for L8E cases have been found to range between 11 and 15 moves.

'''Example Optimal Generator:'''
<pre>U F R U2 R' F' R' F R B L2 B' U2 (13f*)</pre>

== Pros & Cons ==

{| class="wikitable" style="width:100%;"
! style="background:#d5e8d4; width:50%;" | Pros
! style="background:#f8cecc; width:50%;" | Cons
|-
| valign="top" |
* '''Ergonomic Stability:''' No internal slices in the endgame means zero mechanical lockups.
* '''High Move Efficiency:''' Competes directly with Roux for low move counts (~45 moves).
* '''No EO/EP Pause:''' 1-Look L8E removes the transition pause in the final step.
* '''Total Inspection Freedom:''' Full color neutrality allows for the most efficient blocks possible.
| valign="top" |
* '''F/B Fingertrick Mastery:''' Requires high proficiency with Front and Back face rotations.
* '''Mental Load:''' High demand for lookahead during the Zeta Slotting to CMLL transition.
* '''Algorithm Density:''' 1-Look L8E requires a large number of algorithms to cover all cases without slices.
* '''Intuition Threshold:''' Unconventional blockbuilding has a steeper learning curve than CFOP.
|-
|}

== Performance and Statistics ==
* '''Average Move Count:''' 43-50 moves.
* '''Personal Best (Creator):''' 22.00 seconds.
* '''Ideal Usage:''' Speedcubers looking for a high-TPS alternative to Roux or a more efficient alternative to CFOP.

== See Also ==
* [[Roux]]
* [[CMLL]]
* [[Blockbuilding]]
* [[Method Proposals]]

[[Category:Proposed methods]]
[[Category:Blockbuilding methods]]