# advanced pyraminx solution



## fanwuq (Apr 5, 2008)

I've been working on an advanced pyraminx solution. I need some help to develop it. 
Overview:
1.Extended “cross”-- orient the corners(not tips) to the same side while inserting the first edge of the first layer if you see it.
2.insert last 2 first layer edges with one alg, possibly with a commutator, at the same time.
3.Solve with one look LL.

Tips can be corrected anytime.

Advantages to this method:

Easy to learn, not too many algs, very fast with practice, cases are fairly easy to recognize, less moves than all methods that I know of except possibly Michael Gottlieb's “ZBLL pyraminx solution” with 90+ algs.

First step is obvious and intuitional. Rather than just doing the “cross,” it would save a few moves by inserting one edge at the same time if you can see it during preinspection. (I can't always.) Also, if you immediately see a better face to solve, you can do it. (should be no more than 5 moves, excluding correcting tips which I also do at this step.)

2.This step need to be developed. I can already see that some difficult cases for solving the last 2 edges only can be solved faster by doing one of the LL algs. It should be possible to setup to any LL case in a move or 2 and do that, but I don't know if that is better on many cases than pure intuition. Optimal algs are needed. Perhaps you can orient edges at this step to do only sunes to finish LL. Lots of possibilities here. There are many 3 cycle commutator on this puzzle. Some of should help at this step. (Should be less than 8 moves with method complete.)

3.Everyone already do this anyway, i think. (7 moves excluding AUF)

So overall, I would estimate the average number of moves to solve is 17 with this method as opposed to about 26 with my current method which is intuitive First layer, much like the first layer of beginers LBL for 3x3.


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## fanwuq (Apr 6, 2008)

I would be really interested to know if there are any optimal (or at least almost optimal) solvers for any other puzzles than 3x3 cube?


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## Lucas Garron (Apr 7, 2008)

fanwuq said:


> I would be really interested to know if there are any optimal (or at least almost optimal) solvers for any other puzzles than 3x3 cube?


There are.


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## fanwuq (Apr 7, 2008)

thanks, so what are some of them. Please provide links.


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## Kenneth (Apr 8, 2008)

I do orient one centre while placing the first edge, then the same a second time, orient last centre and from there you can do all last four edges in one alg.

But I don't do that last step, I do it as two because algs are so short and recognition is so much slower if you need to look at four edges and also the number of cases increases a lot (around 25 or so). So I orient the last centre and place the last F2L edge (8 cases, 1 solved and 3 mirrors) and then I do ELL (6 cases, 1 solved and 2 mirrors).

My move count is some 18 on average including the trivial tips and not counting lucky cases, including luck it is about 16 I guess.


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## ooveehoo (Apr 9, 2008)

I'm currenty using the normal method for speedsolving, where you correct tips, corrct vertexes(corners), insert FL edges one-by-one and then a one-look LL. This way I average around 13 seconds. But the system I'm developing is a kind of "Pyraminx Heise" and goes like this:

(1. Correct the trivial tips)

2. Build three blocks with an edge and a vertex (corner) piece (it's also possible to make one block with two and one with single edgepiece). This takes usually 3-6 moves and is quite an easy step. No algs.

3. Correct the vertexes, whle preseving the blocks. This is also easy, and takes in most cases 3-5 moves. No algs.

4. Correct the remaining 3 (or 2) edgepieces with an one-look alg. There are 17 4-8 moves long algs in total. The situations are quite fast to recognize, and most of them are really easy, because allmost all of them are R U R' U' variarions/combinations.

My non-lucky record of 4.67 seconds (10 moves) was done using this method. The problem is the time you have to spend thinking about the steps 2 and 3, and so is surely more difficult to master than most systems. But I believe also takes less moves than fanwuq's method.


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## Erik (Apr 9, 2008)

My current (home made/self invented) method is like:
instection time: see how to put together 3 corners (the ones where the tips are attached too) and see how to solve at least one of the edges of that layer, preferably more, sometimes you can see one entire layer. If I can't really see how to built more I'll memorize how to solve some tips instead, so I always make good use of inspection time.
Then solve the first layer or the rest of it using things like RUR' or R'FRF' if you know what I mean, sometimes depending on the rest, you can sometimes skip the last step by putting it in differently. Then solve the Last 3 edges of the U layer and then if necessary solve the tips and then put the pyraminx down and see you did a sub-9


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## qqwref (Apr 9, 2008)

That's almost exactly the method I use in practice Erik  Except I usually do the tips earlier, to take advantage of otherwise wasted delays on my part.

fanwuq: Did you know that Jaap's pyraminx applet comes with an optimal solver? If you set up a position and press the "solve" key it will do one move of an optimal solution, so all you have to do is write down and iterate. That's how I got the algs for my method  I like your idea, though, it could be very fast. Maybe you could also solve the last five edges a bit more Heise-style: solve one edge in the first layer and one in the last, and then the last three in one step (which has a lot of 4-move algs as ooveehoo pointed out).

Oh, and while we are talking about ridiculously efficient methods, Tim Sun's Petrus version got me some really good results. Solve one edge and its associated corners (along with all the tips since the next step is tough); then you have basically 2-gen left, so orient all edges Petrus-style and then solve 2-gen (very easy and intuitive). I don't know the exact movecount for this but I remember being able to average around 13 moves on Tetraminx with it. Orienting edges is the only hard part really, and it might end up requiring some kind of non-color-neutrality if you hope to do a speedsolve.


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## fanwuq (Apr 12, 2008)

I tried the pyraminx at:
http://users.skynet.be/gelatinbrain/Applets/Magic Polyhedra/index.htm
The controls are a bit difficult to get used to, but I'm suprised at my low move count. It's always about 15, never over 20, and once, even a ten. I was simply doing my old method. There's not tips on the simulator, but that doesn't matter.

Thanks Erik and qqwref! I'll try your ways.
I've been so stupid. I could just find 3 algs for partial edge orient for the "LL" while inserting the last FL edge. Then, it's just sune! 

RUR' or R'FRF', I think there is a 3rd one for another case to orient all LL edges, is there? Or would that be just mirror of R'FRF'? So stupid of me. I forgot all about R'FRF'. I was doing only RUR' and RU'R' for the last edge.

Note: I did not have a pyraminx on me.


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## fanwuq (Jul 20, 2008)

Well, my pyraminx broke.  But I came up with a new method for it. It's only 2 looks. One look during pre-inspection, and only one look during solving. 
I got this idea from the ortega method for 2x2.

1. solve one _face_, not layer
2. Permute both layers at the same time.

This really shouldn't be too many algs to learn. There are only 4 possible configurations for the first layer. (ccw cycle, cw cycle, 2 swapped, solved)

There are only 5 cases for the upper "layer" when the bottom is solved. I'm not sure about the numbers of cases for the other types of bottom layer, but total alg number shouldn't be a lot (maybe 20?), recognition should be quite easy.

I'll search for the algs if anyone is *really* interested.

This is much easier than my previous method. Solving one layer is definitely slower than only face. One face is like one look, while one layer can be as much as 3 looks for me.


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## MistArts (Jul 20, 2008)

I have a method yet to be tried out.

1: Solve tips and centers while solving two edges.
2: Finish 4 edges with one algorithm (4!*2*2*2*2/2/2=96 cases) (Correct me if I'm wrong on that.)


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## MistArts (Jul 20, 2008)

fanwuq said:


> Well, my pyraminx broke.  But I came up with a new method for it. It's only 2 looks. One look during pre-inspection, and only one look during solving.
> I got this idea from the ortega method for 2x2.
> 
> 1. solve one _face_, not layer
> ...



Top layer is 3!*2*2*2/2 = 24

Both layer is (4*24)-1 = 95


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## fanwuq (Jul 20, 2008)

MistArts said:


> I have a method yet to be tried out.
> 
> 1: Solve tips and centers while solving two edges.
> 2: Finish 4 edges with one algorithm (4!*2*2*2*2/2/2=96 cases) (Correct me if I'm wrong on that.)
> ...



That would be Michael Gottlieb's "ZB Pyraminx."



> Top layer is 3!*2*2*2/2/3 = 8
> 
> Both layer is (4*8)-1 = 31



What? Are you including AUF or something?


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## MistArts (Jul 20, 2008)

Whoops, I included AUF


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## MistArts (Jul 21, 2008)

Ok, I got the number of cases right this time...(18)

How I figured it out.

3 cases of bottom layer w/o parity. 1 with parity.

When there is no parity, 5 cases for LL.

When there is parity, 4 cases for LL.

(3*5)+(1*4)=19 

19-1 for the solved case.


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## fanwuq (Jul 21, 2008)

I got 20.

solve bottom: 5 LL
ccw bottom: 5 LL
cw bottom: 5 LL
2 swap bottom: 3 LL
solved top: 2 FL


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## MistArts (Jul 21, 2008)

fanwuq said:


> I got 20.
> 
> solve bottom: 5 LL
> ccw bottom: 5 LL
> ...



Actually it would be 21.


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## ooveehoo (Jul 25, 2008)

Does someone have a good alg for orienting 4 edges? Mine just sucks, and takes as many moves as my av. solution, but is essential to a part of my speedsolving method.


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## Stini (Jul 25, 2008)

ooveehoo said:


> Does someone have a good alg for orienting 4 edges? Mine just sucks, and takes as many moves as my av. solution, but is essential to a part of my speedsolving method.



Try this: U L' U L R U' B U' B' R'.


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## fanwuq (Jul 25, 2008)

ooveehoo said:


> Does someone have a good alg for orienting 4 edges? Mine just sucks, and takes as many moves as my av. solution, but is essential to a part of my speedsolving method.



I never needed to flip 4, I used to just solve one layer, and there are just 5 cases to finish:

ccw cycle 
cw cycle
--resolve using Sune or Antisune


ccw cycle flip 2
cw cycle flip 2
-- I forgot the 7 move alg (don't have pyraminx)

pure flip 2
--R'UL'UL'U'LR'
that might not be correct, I tried to trace the feeling of the alg in my head.

So is anyone interested in this 20 alg-1 look solve all method?


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## MistArts (Jul 25, 2008)

I'm more interested in my sortof MGLS method. -.-


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## ooveehoo (Jul 26, 2008)

Stini said:


> ooveehoo said:
> 
> 
> > Does someone have a good alg for orienting 4 edges? Mine just sucks, and takes as many moves as my av. solution, but is essential to a part of my speedsolving method.
> ...



Thanks! Thats great!


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## Kenneth (Aug 4, 2008)

I found a 10 turn 4 edge flip for Pyraminx.

Notation: Hold the cube so there is a U face and a F face, then you got the cornes at R, L, D and B so the turns I use are R, R', L, L', D, D', B, B'

Alg: R' L D' L D R L' B L' B'

There is one more case of 4 edges fliped but this is more common (4 of 5)

For this case I normally use the 8 turn two edge flip twice so this is 6 turns better 

(I get it as my last two steps, the second last one solves the last FL edge and the last step is ELL, sometimes I can solve both in one, to always do it it is some 30 algs to learn, maybe I shall, not sure)

Superflip anyone?, max turns for Pyraminx is 11...


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## mrCage (Aug 6, 2008)

qqwref said:


> That's almost exactly the method I use in practice Erik  Except I usually do the tips earlier, to take advantage of otherwise wasted delays on my part.
> 
> fanwuq: Did you know that Jaap's pyraminx applet comes with an optimal solver? If you set up a position and press the "solve" key it will do one move of an optimal solution, so all you have to do is write down and iterate. That's how I got the algs for my method  I like your idea, though, it could be very fast. Maybe you could also solve the last five edges a bit more Heise-style: solve one edge in the first layer and one in the last, and then the last three in one step (which has a lot of 4-move algs as ooveehoo pointed out).
> 
> Oh, and while we are talking about ridiculously efficient methods, Tim Sun's Petrus version got me some really good results. Solve one edge and its associated corners (along with all the tips since the next step is tough); then you have basically 2-gen left, so orient all edges Petrus-style and then solve 2-gen (very easy and intuitive). I don't know the exact movecount for this but I remember being able to average around 13 moves on Tetraminx with it. Orienting edges is the only hard part really, and it might end up requiring some kind of non-color-neutrality if you hope to do a speedsolve.


 
Hi 

Why is orienting edges hard? Or you talk about orienting more than 2 of them? Flipping only 2 edges takes 8 easy commutator turns ...

I once "fewest moved" the pyraminx in 7 turns, that was way lucky of course

- Per


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## MistArts (Aug 6, 2008)

mrCage said:


> qqwref said:
> 
> 
> > That's almost exactly the method I use in practice Erik  Except I usually do the tips earlier, to take advantage of otherwise wasted delays on my part.
> ...



Per, do you have a solver for pyraminx?

I tried fewest moves for it too. I got 11 before.


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## Swordsman Kirby (Aug 6, 2008)

mrCage said:


> qqwref said:
> 
> 
> > That's almost exactly the method I use in practice Erik  Except I usually do the tips earlier, to take advantage of otherwise wasted delays on my part.
> ...



He means before permuting the edges, which is significantly harder to recognize. That's basically the reason why all of us gave up on this approach.


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## Kenneth (Aug 6, 2008)

qqwref said:


> Oh, and while we are talking about ridiculously efficient methods, Tim Sun's Petrus version got me some really good results. Solve one edge and its associated corners



That's the same as my first step, the second I do an adjacent edge and a third corner (or "centre", some like to call them that). I wrote about it earlier. The last corner I do while I look for the third FL edge that I solve as 7 cases, then ELL (5 cases). I mostly practice inspection and got methods to see the first two steps in some 80% of the solves, the last two steps is pure brute force and really fast. Recognition is almost instant and in most of my algs I got no regrips and I practice to not regrip between the two last steps, that I find "learnable" =)

Average is currently 10 secs for my best 3(5)'s and 11 secs for 10(12)'s, still I'm not a wery fast cuber.

A comon method is to place two edges and then orient corners using the third edge's place as a keyhole, then place the third edge and do ELL = the last two steps are the same as mine but comparing the first two is like comparing kehole F2L to Fridrich F2L, I simply do corner-edge pairs as my first two steps


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## mrCage (Aug 12, 2008)

Hi 

And here's a superflip (flip all edges) on the pyraminx:

(R' L U)*3

See the image below. R turns the R tip together with the (middle) layer next to it. Same with L and U. R' mean counterclockwise turn (2 steps clockwise ..)






Regards,

Per


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## fanwuq (Aug 19, 2008)

For my "Ortega"-like method:

I found that building one face is quite a bit easier than building a layer. I'm not very good at either, but I average about 5 moves for face and 10 for layer. Recognition of the algs is quite easy. I can recognize almost as fast the the previous method, but I haven't looked for the algs yet. This I expect to yield about 12 move solutions on average once you get good at it.


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## MistArts (Aug 20, 2008)

I'm almost done learning my method. I don't use all of the 95 algs. I just use 2 commutators and algorithms for special cases.


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## TMOY (Aug 20, 2008)

Stini said:


> ooveehoo said:
> 
> 
> > Does someone have a good alg for orienting 4 edges? Mine just sucks, and takes as many moves as my av. solution, but is essential to a part of my speedsolving method.
> ...



A bit longer but with no B: (LUL'R)^3.


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## fanwuq (Aug 21, 2008)

MistArts said:


> I'm almost done learning my method. I don't use all of the 95 algs. I just use 2 commutators and algorithms for special cases.



Beat my pathetic NR next competition!


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## MistArts (Aug 21, 2008)

fanwuq said:


> MistArts said:
> 
> 
> > I'm almost done learning my method. I don't use all of the 95 algs. I just use 2 commutators and algorithms for special cases.
> ...



Don't worry...you still have 3 months with it...


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## deadalnix (Oct 16, 2009)

Topic resurection !

Does anyone know where a list of all the cases for last 4 edges can be found ?


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## qqwref (Oct 16, 2009)

http://www.columbia.edu/~ts2578/speedcubing/pyral4e.html


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## deadalnix (Oct 16, 2009)

Thank you !


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## Shiv3r (Jun 24, 2016)

I got a pyra for my birthday,(got it in the evening ~ 6:30pm) and by the time I went to bed I had figured out a way to solve it by myself(It seems kinda like a simplified 1-flip method). so here it is:
1.solve 2 edges around 1 center.
2.using inverted U moves(hold the U center and twist the bottom) move around and fix the centers
3.set up and solve the center with an alg I came up with: L' R'(I used to do R2) L R.
4.solve the last 3 edges using commutators like R L R' L' until either it is solved or you get a pure flip. Then use a commutator to solve the pure flip.


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## Hssandwich (Jun 25, 2016)

Shiv3r said:


> I got a pyra for my birthday,(got it in the evening ~ 6:30pm) and by the time I went to bed I had figured out a way to solve it by myself(It seems kinda like a simplified 1-flip method). so here it is:
> 1.solve 2 edges around 1 center.
> 2.using inverted U moves(hold the U center and twist the bottom) move around and fix the centers
> 3.set up and solve the center with an alg I came up with: L' R'(I used to do R2) L R.
> 4.solve the last 3 edges using commutators like R L R' L' until either it is solved or you get a pure flip. Then use a commutator to solve the pure flip.


That's the keyhole method.


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