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Master Pyraminx Speedsolving- Creating the Kyoo Method

Kyoobies

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May 20, 2022
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23
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Southern California
Master Pyraminx! So much potential for speedsolving, and such a good non wca option.

As of late, I've been working hard at making my own speedsolving method (technically I started it forever ago but am only really working hard at it nooowww... :V ), and I thought here would be a great place to share it. It seems there's quite a lot of love for non wca, and I feel like the forum format will be good for posting small gradual updates and chatting with anyone else interested. :D

First off, here's a quick overview (not a tutorial yet, just an overview as fast as possible) of the idea behind the method:
Kyoo Part 2 on Reddit.

As for what I'm working on right now, I have a google doc of all the L3E + face center cases, with algs generated with ksolve+. Atm it's 29 pages (lol) and I just need to sort through and find the best algs. In that regard there are 2 options, as algs can be done either purely as an L3E case, or you can often do a setup B move, the best alg for the case, and undo the setup move. This may be viable too as you could cancel into the B setup right after 1flip; but I don't know if that's actually practical or any faster yet. I'll have to try applying it when I can.

The second thing I'm working on is 1flip + parity. Essentially parity boils down to a twisted tip center, but if you solve the rest of the reduced pyraminx (which is still possible) you end up with face centers cycled around. Instead of that, if you just solve 1flip with the face centers correct in the end (either solved or in a double swap) then you can leave 1 of the tips twisted. And that gives you a lot of possibilities of how to actually do 1flip -and especially how to do it optimally- but with the limited freedom of a twisted tip. It should all just be the normal 1flip cases, but with different recognition applied and picking your case differently. I can explain it more how that works when I release a post about all the best cases, and why they work for the curious.

I'm also not sure what angle I should do 1flip from but I'm going to try doing it from that side grip I used in the reduction. I'd appreciate some thoughts in that regard from people more experienced with pyraminx in general.

And some other stuff, I'm still experimenting with the best way to pair the edges in reduction, as well as modding some hardware. I still haven't figured out all that does what in the hardware, but I'm making progress. Also I need to buy magnets lol.

Alright, time to keep at it!
 

Kyoobies

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May 20, 2022
Messages
23
Location
Southern California
Oh hey some people have experimented with reduction using that R face turn + U moves before, cool :O
Kit Clemet's Video on his method

And lol it was posted like 20 days after my original reddit post (I'm sure he was using it comfortably before that haha), what amusing timing lmao. I hadn't thought that grip & turning was used really, but it makes sense as it's the best way to free the puzzle up to do reduction style solving. Everything else limits the movements too much.

How fun indeed
 

Kyoobies

Member
Joined
May 20, 2022
Messages
23
Location
Southern California
Oh hey some people have experimented with reduction using that R face turn + U moves before, cool :O
Kit Clemet's Video on his method

And lol it was posted like 20 days after my original reddit post (I'm sure he was using it comfortably before that haha), what amusing timing lmao. I hadn't thought that grip & turning was used really, but it makes sense as it's the best way to free the puzzle up to do reduction style solving. Everything else limits the movements too much.

How fun indeed
Ohhhhhhhhh interesting. So his choice not to start with solved edges relative to a tip center opens up the Rw' D Rw' move, and opens up easy edge flipping to help the reduction go smoother. And should help the start be easier. But it means that the flow into the reduced pyraminx stage is hurt because you aren't starting partially solved.

And the 1flip + parity into L3E + centers can still apply to his approach as well, assuming they work out to be good and fast. Also he's got good ergonomics for his 3 center cycle cases, that's the best I've seen it finger tricked so far (excluded my janky table abuse version that I really don't want to exist lol)

How very fun and interesting :3
 

abunickabhi

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WCA
2013GHOD01
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Master Pyraminx! So much potential for speedsolving, and such a good non wca option.

As of late, I've been working hard at making my own speedsolving method (technically I started it forever ago but am only really working hard at it nooowww... :V ), and I thought here would be a great place to share it. It seems there's quite a lot of love for non wca, and I feel like the forum format will be good for posting small gradual updates and chatting with anyone else interested. :D

First off, here's a quick overview (not a tutorial yet, just an overview as fast as possible) of the idea behind the method:
Kyoo Part 2 on Reddit.

As for what I'm working on right now, I have a google doc of all the L3E + face center cases, with algs generated with ksolve+. Atm it's 29 pages (lol) and I just need to sort through and find the best algs. In that regard there are 2 options, as algs can be done either purely as an L3E case, or you can often do a setup B move, the best alg for the case, and undo the setup move. This may be viable too as you could cancel into the B setup right after 1flip; but I don't know if that's actually practical or any faster yet. I'll have to try applying it when I can.

The second thing I'm working on is 1flip + parity. Essentially parity boils down to a twisted tip center, but if you solve the rest of the reduced pyraminx (which is still possible) you end up with face centers cycled around. Instead of that, if you just solve 1flip with the face centers correct in the end (either solved or in a double swap) then you can leave 1 of the tips twisted. And that gives you a lot of possibilities of how to actually do 1flip -and especially how to do it optimally- but with the limited freedom of a twisted tip. It should all just be the normal 1flip cases, but with different recognition applied and picking your case differently. I can explain it more how that works when I release a post about all the best cases, and why they work for the curious.

I'm also not sure what angle I should do 1flip from but I'm going to try doing it from that side grip I used in the reduction. I'd appreciate some thoughts in that regard from people more experienced with pyraminx in general.

And some other stuff, I'm still experimenting with the best way to pair the edges in reduction, as well as modding some hardware. I still haven't figured out all that does what in the hardware, but I'm making progress. Also I need to buy magnets lol.

Alright, time to keep at it!
Interesting!

I like the method that Harsha Paladghu uses. It is quite efficient.
 

Kyoobies

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Joined
May 20, 2022
Messages
23
Location
Southern California
Interesting!

I like the method that Harsha Paladghu uses. It is quite efficient.
Yeah Harsha's method is awesome, it's well proven and is probably the best base for a method focusing on commutators/3 cycles directly to solved.

I'm gonna real look into comparing things eventually but to overview without going deep, my method is pretty much a gamble to see if reduction style solving taken to completion can catch up with his. People have experimented with reduction and while it has a lower move count (I'm pretty sure this agreed upon) it's a lot tougher to actually apply. So it's not the current top, but I see potential.

It's also just fun to make this and I think the solve ends up more enjoyable, so if nothing else I can have a good time and prove for sure that others are better. Or maybe mine will work out to be the best, or maybe they'll be super close and both good. We'll have to wait and see x3

And nomatter what happens, the puzzle needs more love and attention <3
 

Kyoobies

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May 20, 2022
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Southern California
Eyyyye translated 1flip into a side grip version to fit with the grip it's already in. Might need to adjust some or find nice alts, and definitely need to make fingertricks. But more importantly I need to math out optimal parity manipulation versions; though that should be easy enough. Baby steppps

Master Pyraminx Side Grip 1Flip

Same color on front; edge insert- Rf’ U’ R’ U R
Back color on front; edge insert- R’ U’ R U

(Pure) (2flip)- S U L’ U’ L
L’ U L U’ H

(1 CntrClk)- U’ Rf’ (U’ R’ U R)

(1 Clk)- U Rf’ (R’ U’ R U)

(2 Together)- (bottom pieces to the back) U Rf’ U’ Rf’ (U’ R’ U R)
(bottom pieces to the front) U’ Rf U (R’ U’ R U)

(2 Apart)- (back) U’ Rf’ U (U’ R’ U R)
(front) U Rf U’ Rf (R’ U’ R U)

(2 CntrClk)- U’ Rf U’

(2 Clk)- U Rf’ U

(Together + CntrClk)- U’ Rf’ U Rf’ U’

(Together + Clk)- U Rf U’ Rf U

(3 CntrClk)- U’ Rf’ U’ Rf’ U’

(3 Clk)- U Rf U Rf U
 

Kyoobies

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May 20, 2022
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I aso found a vital move trigger for covering the dead zones/impossible cases in my reduction step.


I quite enjoy it and have lovingly nicknamed it Smexy Move; but I'm certainly open to any suggestions haha xP

Oh and it's awesome for doing parity/a three cycle of top wings from a home grip if you add U moves with the left index, so even other methods could use it. :D
 

Kyoobies

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Random rambling on break out work, just to get stuff out. Still working on picking the best 1flip + parity cases and I wanna explain it asap. Anyway-

Found a nice alg for finishing the last 3 wings, when they're on 2 edges instead of 3. If you do it twice in a row, it also solves the case of 2 super flipped edges which is super cool.

Also experimenting with a different way to do Rf (R face) turns that stays in home grip.

For the first 2 edges, I'm finding there's a lot of ease and freedom if you only solve 1 edge and connect it to the tip center, and put the tip center in your left hand. Doing the second edge like that and inserting it without regripping seems easy, and it's probably a good approach for the start. 2 edge and connecting them both all intuitively/optimally may not be viable, or at least always viable/viable for intermediate solving. Doing just 1 and then the second also flows to the next steps nicely it seems.

As for the reduction step, I need to actually commit and practice and figure out what really works.
But I think a good default that I'm going to try is solving the first half edge, and placing it on the bottom right with the open wing in the back. This puts the solved stuff into a blind spot, and gives you 3 nice options for pairing the next wing. Either you do a U/U' if there's one set up, you do a smexy move/inverse smexy, or you do Rf' and then U/U'. It's a lot of options and should be good for making a second half edge fast.

The other option/alternative option for different cases would be to put the first half edge in the top left, with the open wing on top. That lets you do any Rf move into U/U' so there's guaranteed to be something, but you also have the half edge trapped in the top left and it might not be the easiest to set up with other half edges (though I could totally be wrong if you set up to smexy move, smexy move is quite new to me)

And speaking of smexy move, I did counter clockwise parity (a 3 cycle of the wings in the tip, and an extra U') in under a second a few times last night. Smexy U' smexy U'
I'm gonna try to get both directions sub 1, then film and share it.

Fun stuff! :D
 

Kyoobies

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May 20, 2022
Messages
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Location
Southern California

Here's the counter clockwise parity sub one second.
Alg is (inverse smexy) U' (inverse smexy) U'
:3
Clockwise is next but it's a tad slower. It's close though. And most importantly, smexy move is viable hah >3>


EDIT: It's actually inverse smexy move omg I forgot my own trigger lmao. It's faster not because it uses the better smexy, but because the U' is easier than U. That's why it confused me. I'm a big dumb haha
 
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Kyoobies

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Southern California
2 new things, first off here's a trigger idea for doing some last 3 wings cases more algorithmically. I'm pretty sure it's just commutators at this point lol, but it's the ergonomics that matter imo. You can also do a small regrip at the start to do R instead of R', and it completely changes what gets moves around and how. It changes it to cycling around 3 edges, instead of 2 edges with 1 of the wings flipped. And you can start with a cube rotation instead of an Lw, to cancel into the algs using the top tip instead of the front right.

Lots of options, all ergonomics optimized in their intention. The algs also don't affect the rest of the puzzle except for a tip center, so lookahead into 1flip should be really nice.

 

Kyoobies

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May 20, 2022
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2nd, I applied the parity manipulation to all the different 1flip cases. It's still the standard 11 cases, but applied differently.

So for an explanation of how it works and what's happening, it's important to know what's happening. The issue is that in doing reduction, you create an impossible case for the jing's pyraminx (a pyraminx with face centers). Normally, doing a turn on a jing's pyraminx simultaneously rotates a tip center as well as the face centers, in the same fashion. 1 clockwise turn, rotates both of them clockwise once for instance. These turns loop around on the 3rd turn, so we can give them a value of 1 (doing 1 clockwise turn), 2 (1 counterclockwise turn; or 2 clockwise turns), and then 3 is actually back to zero.

The reason you get an impossible case is that these cycles of three get desynced from each other; something that shouldn't ever happen. So when your solve is finished, one of those two piece types can be rotated impossibly. Either a 3 cycle of face centers, OR you make sure the faces are solved and you end up with a twisted tip center. Both of these can be twisted in either direction (clockwise or counterclockwise), or just solved.

So what I'm working to do is to force a case where a tip center is the one solved incorrectly in situations of parity; while face centers are always correct. This is something that's much easier and much faster to solve than cycling face centers. Doing this also allows you to solve last 3 edges & your face centers in a single algorithm set, something entirely unreasonable to do with cycling 3 face centers as well.

.
.

So for actually applying it. What you actually want to do for 1flip is not solve all 3 tip centers- instead you solve just 2 tip centers and solve face centers into a not parity state. If you have parity, the 3rd tip center will then stay twisted and can be fixed after.

So first you inspect for what move would be required on the puzzle to solve face centers. Either no moves (solved already, or in a double swap) which we will assign a value of zero. This is because it takes zero twists, or something that ends in a value of zero, to solve. [As an example. A clockwise twist is a value of 1. So three of them = a value of 3, which we change to zero. 3 counterclockwise twists would add up to a value of 6, which reduces down to a value of zero after removing 3 from it twice].

If you need 1 clockwise twist (a value of 1) to solve the centers, then you have to pick any algorithm that solves any two tip centers AND has a value of 1. [For example, 2 counterclockwise twists adds up to a value of 4. Subtract 3 since 3=0, and we end up with a value of 1. A single clockwise twist is a value of 1, and 2 counterclockwise twists is also a different way to achieve a value of 1).

Counterclockwise to solve centers, same thing with a value of 2.

.
.
.
.

SO with that in mind, here are what seem to be the best choices for applying every possible case-
1flip_case_numbers.png

Master Pyraminx Side Grip 1Flip

Same color on front; edge insert- Rf’ U’ R’ U R
Back color on front; edge insert- R’ U’ R U

[Case 1, value 0](Pure) (2flip)- S U L’ U’ L
L’ U L U’ H

[Case 2, value 2](1 CntrClk)- U’ Rf’ (U’ R’ U R)

[Case 3, value 1](1 Clk)- U Rf’ (R’ U’ R U)

[Case 4, value 0](2 Together)- (bottom pieces to the back) U Rf’ U’ Rf’ (U’ R’ U R)
(bottom pieces to the front) U’ Rf U (R’ U’ R U)

[Case 5, value 0](2 Apart)- (back) U’ Rf’ U (U’ R’ U R)
(front) U Rf U’ Rf (R’ U’ R U)

[Case 6, value 1](2 CntrClk)- U’ Rf U’

[Case 7, value 2](2 Clk)- U Rf’ U

[Case 8, value 2](Together + CntrClk)- U’ Rf’ U Rf’ U’

[Case 9, value 1](Together + Clk)- U Rf U’ Rf U

[Case 10, value 0](3 CntrClk)- U’ Rf’ U’ Rf’ U’

[Case 11, value 0](3 Clk)- U Rf U Rf U

PURE CASES (0 value/No twists to solve)

0(Pure) (2flip)- S U L’ U’ L
L’ U L U’ H

(1 CntrClk)- DONE

(1 Clk)- DONE

0(2 Together)- (bottom pieces to the back) U Rf’ U’ Rf’ (U’ R’ U R)
(bottom pieces to the front) U’ Rf U (R’ U’ R U)

0(2 Apart)- (back) U’ Rf’ U (U’ R’ U R)
(front) U Rf U’ Rf (R’ U’ R U)

(2 CntrClk)- CASE 10

(2 Clk)- CASE 11

(Together + CntrClk)- CASE 10

(Together + Clk)- CASE 11

0(3 CntrClk)- U’ Rf’ U’ Rf’ U’

0(3 Clk)- U Rf U Rf U


Clockwise CASES (1 value/Clockwise twist to solve)

(Pure)- CASE 3

(1 CntrClk)- CASE 6

1(1 Clk)- U Rf’ (R’ U’ R U)

(2 Together)- CASE 7

(2 Apart)- CASE 7

1(2 CntrClk)- U’ Rf U’

(2 Clk)- CASE 3 OR 9

(Together + CntrClk)- CASE 8

1(Together + Clk)- U Rf U’ Rf U

(3 CntrClk)- CASE 6

(3 Clk)- CASE 9


CounterClockwise CASES (2 value/CntrClk twist to solve)

(Pure) CASE 2

2(1 CntrClk)- U’ Rf’ (U’ R’ U R)

(1 Clk)- CASE 7

(2 Together)- CASE 6

(2 Apart)- CASE 6

(2 CntrClk)- CASE 2 OR 8

2(2 Clk)- U Rf’ U

2(Together + CntrClk)- U’ Rf’ U Rf’ U’

(Together + Clk)- CASE 9

(3 CntrClk)- CASE 8

(3 Clk)- CASE 7
 

Kyoobies

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May 20, 2022
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Location
Southern California
I plan on making a better reference visual to use as a resource and all that when I can, but for now there's a functional reference for 1flip+parity that exists.:cool:😁

Next up is sorting through my list of generated algs for the best (or at least adequate lol) algs for l3e + face centers. They're ready but I just need to find the good ones haha.
And then I'll work on making a good reference for learning from easily, and optimize my plans for priorities during reduction/doing the start/etc etc.

:3
 

Kyoobies

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Solving "Pure_Flip" (Triple sledge)
(R' L R L')x3


Solving "Pure_Sledge" (Double hedge)
(L R' L' R)x2


Solving "Sledge_Flip_Left"
B R' L R L' B'
R L' R2' L2 R L2' R L R'


Solving "Sledge_Flip_Right"
B' R' L R L' B
L' R L R2' L R2 L2' R' L


Solving "Sledge_Flip_Down"
R' L R L'


Solving "Pure_2Flip"
U' R U R2' L R L2' U L U'


Solving "2Flip_Flip_Left"
L R' L' R U' R U R'


Solving "2Flip_Flip_Right"
R' L R L' U L' U' L


Solving "2Flip_Flip_Down"
R L R2’ L' R U' R' U R


Solving "Pure_Counter_Clockwise"
U R' L R L' R U R' U
U L' U L R' L R L' U


Solving "Counter_Clockwise_Flip_Right"
R' L R L U L U'


L3EC cases done! Here's viable algs for all of the case. I also brute forced some triple 3 cycle cases as alternate solutions, but only 1 or 2 seem viable imo.

Next up I'm gonna post them again with execution for each case, along with the 1flip cases. As well as general reduction things I do.

But with that, Kyoo is a functional method! 🥳
 

Kyoobies

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May 20, 2022
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Location
Southern California
Alright!

Progress has been slow lately as I'm busy with life, but it's given me a lot of time to thing about things and brainstorm ideas. And just a couple days ago, I think I figured out how to completely change the approach to pyraminx stage and work in L4e!

So, I understand the puzzle a lot more and I looked at it with fresh eyes; and there's 2 things I've thought of.
-First of all, you can do pseudo V-first that just requires a Bw move at the end of the solve. It doesn't have to be a true V. That makes orienting 2 tip centers after reduction way easier, often (if 1 is already oriented) only 2 moves! It usually take 2 moves just to *set up* for 1flip, let alone do the alg as well.
-And second, if you completely ignore the top tip center, there are actually only 2 times the amount of cases as regular L4e. Which is completely reasonable, especially with the ease of L4e algs. If you account for pre AUF, you only have 2 cases for face centers. All face centers solved, and face centers needing to flip.

These algs may be pretty good as well, since there's a lot less pieces already solved so there's greater flexibility in solving face centers at the same time.

And this way, parity will always be on the top tip and easy to solve ergonomically. As well as be easy to predict with practice.

So this is my next project, and with batch solver it's gonna be way easier to generate the cases then before! L4E+C, exciting!

.

Some other things as well, I've found a few ways to visualize the puzzle, I've got my camera setup working great, and I even have a stickered puzzle in the mail to swap pieces for blank black ones in demo videos for clarity. More stuff on the way, references and everything!
 
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Kyoobies

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May 20, 2022
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Location
Southern California
Oh and it's also only like, 3 moves to force a different set. So for learning purposes, the amount of cases can easily be cut it half with minimal impact! Algorithm subdivision woohoo! (That's actually really important to me lol because making beginner and intermediate friendly versions is important for getting new solvers into the puzzle xP)
 
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Kyoobies

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May 20, 2022
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Location
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Batch solver is absolutely not happy with me, and I'm ready to die lol.
BUT
I have finally managed to gen a bunch of algs for l4e+c. It's gonna be a ton of work to go through 1 at a time and make images for reference and pick the best algs, as well as filter through all the duplicate nonsense I had to make to get batch solver even working lol.

But more algs are here, and soon Kyoo will have a second method/set of algs for the reduced pyraminx stage!
 
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