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 Post subject: Solving the Pyraminx Crystal [SOLVED]
PostPosted: Fri Sep 14, 2007 6:10 pm 
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1.1.3


So I've been messing with a lot of applets on GelatinBrain's website. One of which being the Pyraminx Crystal Applet.

Now, so far I've gotten all but 5 corners and 10 edges solved. I have a feeling I had to solve the top corners before putting together the middle.


Has anyone solved this intuitively? I know there's a solution out there somewhere. (George sent me the PDF a while back, but I think I accidentally deleted it. :P)


[Edit] So I've solved all the corners, and all edges except the top 'layer' 10.

[Edit2] I've found I can permute, but not orient the bottom 5 edges in the top 'layer'. Perhaps I can do some 3 cycles that go into the top 5. This would be much easier with a tangible puzzle.

[Edit3] After figuring out some nice 3 cycles, I have solved all but 2 edge pieces in the bottom part of the top 'layer'. They are flipped. I don't have a clue how to handle this one. Hmm....

[Edit4] Solved in 35 minutes and 47 seconds. 421 moves were done to solve. An explanation of the solution is in the following post.

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Last edited by Noah on Wed Sep 26, 2007 2:05 pm, edited 2 times in total.

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 Post subject:
PostPosted: Fri Sep 14, 2007 7:25 pm 
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Sadly, under an hour later, I solved the puzzle, making this thread pointless. So now I'm going to write up how I solved the puzzle. I won't give exact details on some things, because I'm horrible at explaining.
---------------------------------------

How I break down the Pyraminx Crystal.

3 Layers:

Top Layer:
- 5 Upper Top Layer Edges
- 5 Top Layer Corners
- 5 Lower Top Layer Edges
Middle Layer:
- 5 Upper Middle Layer Corners
- 5 Middle Layer Edges
- 5 Lower Middle Layer Corners
Bottom Layer:
- 5 Upper Bottom Layer Edges
- 5 Bottom Layer Corners
- 5 Lower Bottom Layer Corners

---------------------------------------
1) Solve bottom layer corners.
2) Solve lower bottom layer edges.
3) Solve 4 of the 5 upper bottom layer edges.
4) Use the open spot (in the upper lower layer edges) to place the next layer of corners. (Lower middle layer corners)
5) Some how pair up the last upper bottom layer edge and the lower middle layer corner it belongs with, and place it in.
6) Place the remaining 5 upper middle layer corners.
7) One by one, place the middle layer edges.
7a) Place a middle layer edge in the bottom of the top layer. You can do this by taking out an upper middle layer corner, moving it around in the upper layer and replacing it. Edge orientation matters, so you may also have to correct edges this way.
7b) Break the first layer, and turn the top layer to place the edge in, and fix the first layer
7c) Repeat until just the top layer remains.
8) Orient remaining (Top layer) corners using sune, or similar algorithms. Watch out. Make sure you keep everything you already solved in tact.
9) Permute top layer corners. Same as beginners megaminx solution step. Involves taking out corner, turning top, and replacing next corner, so one and so forth (3 cycle).
10) You have 10 edges left. You use a 3 cycle affecting only the lower top layer edges.
10a) Find your starting edge in the lower top layer. You notice only 2 types of turns will affect this piece. A top layer turn and one of the bottom half turns. I will give a short algorithm using the top layer as U and the other turn as R. [RUR'URU2'R'] That should 3 cycle edges in the bottom of the top layer.
10b) Use one of the turns adjacent to the top layer to bring a upper top layer edge into the lower top layer of edges. You can now use the 3 cycle to move a correct edge in. Be careful that when you undo the set up move that only the top layer edges were affected.
11) Use those steps to solve the upper top layer edges.
12) Now all that is unsolved is the lower top layer edges. Use the 3 cycle to place the remaining edges into the correct spots.
13) In my case, of the remaining edges, two were flipped. I can't remember exactly how I fixed this.
---------------------------------------

By no means is this a tutorial on how to solve the Pyraminx Crystal, and most likely is it not a efficient solution. All of this was done by intuition.



[EDIT] I have mastered my method. I can't really describe it.

As for the double edge flip, I do a 3 cycle, double turn a couple of the locations in the 5 loop. It's a lot of just looking at what you're doing.

I've gotten under 10 minutes now. I've aiming for under 7:30 on the applet. If I ever get to play with one, I hope under 5.

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Fridrich
3x3 PB 22.63
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 Post subject:
PostPosted: Sat Sep 15, 2007 10:15 am 
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hihi, im happy i got a solution-booklet in pdf for it :)


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 Post subject:
PostPosted: Sat Sep 15, 2007 10:20 am 
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Nice job, Noah! I can't hope to solve things like that on applets that aren't free rotating, so I guess that's just a puzzle I won't get to solve.

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 Post subject:
PostPosted: Sat Sep 15, 2007 11:06 am 
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Speedy McFastfast wrote:
Nice job, Noah! I can't hope to solve things like that on applets that aren't free rotating, so I guess that's just a puzzle I won't get to solve.
Dude, click and drag. It free rotates fine. Just ignore the arrows.

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 Post subject:
PostPosted: Sat Sep 15, 2007 11:17 am 
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Why not solve like an impossiball + pyraminx?

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[02:25] <fusion> does look ahead on a 3x3 make someone faster?
[02:25] <Swordsman_Kirby> Yes.
[02:25] <fusion> maybe i should try that


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 Post subject:
PostPosted: Mon Sep 17, 2007 1:16 pm 
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I think someoone should retract that statement it will be just another puzzle I wont be able to solve...all because of the glorious news from mefferts.

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 Post subject:
PostPosted: Mon Sep 17, 2007 3:54 pm 
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Well now you can solve in real life, I think. Mefferts said he was gonna release it, I think...

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 Post subject:
PostPosted: Mon Sep 17, 2007 4:39 pm 
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Solved it Saturday in real life. :)

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single attempts => 4x4 - 1:21.78, 5x5 - 2:05.11, magic - 1.38, master magic - 5.03


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 Post subject:
PostPosted: Mon Sep 17, 2007 4:56 pm 
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UMichSpeedCubist wrote:
Solved it Saturday in real life. :)
Whose did you play with? Just curious.

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Started cubing Oct 15 '05

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 Post subject:
PostPosted: Mon Sep 17, 2007 11:19 pm 
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skenegee's.

I did corners first, using what I use for megaminx, but centers dont' matter. And then I used a simple commutator for the edges. Near the end it required a lot of setup moves. At the very end I had to flip two edges... that took a while.

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single attempts => 4x4 - 1:21.78, 5x5 - 2:05.11, magic - 1.38, master magic - 5.03


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 Post subject:
PostPosted: Tue Sep 18, 2007 8:28 am 
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UMichSpeedCubist wrote:
skenegee's.

I did corners first, using what I use for megaminx, but centers dont' matter. And then I used a simple commutator for the edges. Near the end it required a lot of setup moves. At the very end I had to flip two edges... that took a while.



I've figured out you have to do a 3 cycle, the flip one of the edges by doing a single set up move, then undoing your 3 cycle, and then undoing the set up move.

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 Post subject: The Crystal Method
PostPosted: Mon Jul 14, 2008 5:02 pm 
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UMichSpeedCubist wrote:
I did corners first, using what I use for megaminx, but centers dont' matter. And then I used a simple commutator for the edges. Near the end it required a lot of setup moves. At the very end I had to flip two edges... that took a while.


Just got mine this weekend and that's the exact method I used. Anybody got some cool algs or methods to share?

Chris


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 Post subject: Re: Solving the Pyraminx Crystal [SOLVED]
PostPosted: Mon Jul 14, 2008 5:55 pm 
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This is an interesting thread revival. :)

the way the slices intersect basically begs one to use corners-first then simple edge comms.

here's something mildly interesting... a similar alg to the one used to rotate one corner on the SuperX (R UFL R' UFL R UFL R' UFL) or rotating one corner on a pyraminx (three cycle edges then turn so edges are solved) can be used to 5-cycle the pieces around the bottom of a layer, thus making a sort of "megaminx twist". So if you want to just multiply your megaminx solution length by 10 you can solve it like that ;)

Noah's block building start farther up this thread is like something I'd recommend if you don't want to do straight-up corners-first.

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 Post subject: Re: Solving the Pyraminx Crystal [SOLVED]
PostPosted: Mon Jul 14, 2008 6:49 pm 
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I pretty much solve things using block building/edge insertion up until I've got 3 layers left that contain edges. The bottom layer is basically slots between solved corners (I solve all corners by now), the middle layer is just there, and then there are the LL edges left over.

I use the bottom slots to shoot LL edges into their correct places, and then solve all of these slots but one or two. After that I use the remaining slots to solve the middle layer of remaining edges. Finally, I solve the last slot and the last 2 remaining edges. I can do the parity, but I always mess up somehow and it takes forever.

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 Post subject: Re: Solving the Pyraminx Crystal [SOLVED]
PostPosted: Tue Jul 15, 2008 11:08 am 
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I found when I was first trying to solve it that I would end up with all solved but 2 flipped pieces, in the correct place.

I think it was Noah who told me about doing 2 3 cycles, a set up move and then undoing the 3 cycles.
If anyone gets stuck on this step I think Michael Gottlieb has a video of him solving the crystal on youtube, the last step he does is a text book example of what I'm talking about.

Apart from this step, its a pretty straight forward puzzle IMO.
3 cycle ------------> Victory! :D


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 Post subject: Re: Solving the Pyraminx Crystal [SOLVED]
PostPosted: Tue Jul 15, 2008 2:14 pm 
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This puzzle lends itself relatively nicely to commutators.

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[02:25] <fusion> does look ahead on a 3x3 make someone faster?
[02:25] <Swordsman_Kirby> Yes.
[02:25] <fusion> maybe i should try that


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 Post subject: Re: Solving the Pyraminx Crystal [SOLVED]
PostPosted: Thu Jul 17, 2008 1:58 pm 
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Hi :-)

The 2 flipped LL edges are also solvable by a commutator, though not a very short one. It is rather easy to get lost on it :?

- Per

PS! Yes i had my copy in the mail today :P

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 Post subject: Re:
PostPosted: Fri Aug 08, 2008 10:33 am 
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UMichSpeedCubist wrote:
skenegee's.

I did corners first, using what I use for megaminx, but centers dont' matter. And then I used a simple commutator for the edges. Near the end it required a lot of setup moves. At the very end I had to flip two edges... that took a while.


ehmmm....I have done the corners in a few minutes like megaminx...now the edges....what commutator did you use for the edges?....please.... :oops:


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 Post subject: Re: Solving the Pyraminx Crystal [SOLVED]
PostPosted: Fri Aug 08, 2008 12:58 pm 
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An easy 3 cycle that goes like R U R' U'. If you have solved a pyraminx before it should be pretty easy.

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 Post subject: Re: Solving the Pyraminx Crystal [SOLVED]
PostPosted: Sat Aug 09, 2008 9:36 am 
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Thanks all guys!! :) Today finally I solved my Pyraminx crystal!!!....First I placed the corners using the megaminx algorythms, then i placed the edges (that took more time...) using this simple commutators LRL'R' and R'L'RL.... :P
I want to thank all guys that helped me in this topic with their suggestions.....
now I can think at 7x7x7 cube...it's really amazing and much better then 6x6x6 in rotations.... :lol:


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 Post subject: Re: Solving the Pyraminx Crystal [SOLVED]
PostPosted: Mon Aug 11, 2008 5:08 pm 
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Italrubik wrote:
Thanks all guys!! :) Today finally I solved my Pyraminx crystal!!!....First I placed the corners using the megaminx algorythms, then i placed the edges (that took more time...) using this simple commutators LRL'R' and R'L'RL.... :P
I want to thank all guys that helped me in this topic with their suggestions.....
now I can think at 7x7x7 cube...it's really amazing and much better then 6x6x6 in rotations.... :lol:


Yay. I solved mine today for the first time too. Took far too long. Very satisfying to have done it though :) I placed corners (intuitive + commutators for last layer) and for edges I used the basic R'LRL' 3 cycle with setup moves. That just about did it really.


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 Post subject: Pyraminx Crystal - Last Layer Algorithms
PostPosted: Wed Aug 20, 2008 4:35 pm 
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Pyraminx Crystal - Last Layer Algorithms

Here is one method for solving the last layer of the Pyraminx Crystal. I hope that it will be of some interest to fans of this puzzle, both speedsolvers and leisurely solvers -- anyone who enjoys comparing methods and solving as efficiently as they can. Suggestions, corrections, improvements, and alternatives are welcome and encouraged.

Overview
Stage 1. Orient corners.
Stage 2. Permute corners.
Stage 3. Lower edges. Includes fixing the orientation of moved edges - ignoring any lower edges that are correctly positioned but flipped.
Stage 4. Permute upper edges (ignoring their orientation).
Stage 5. Flip edges.

Average Turn Count (face turns / fifth turns):
Stage 1. 9.01/9.57
Stage 2. 12.32/13.27
Stage 3. 28.91/31.69
Stage 4. 7.52/8.00
Stage 5. 10.96/18.41
Total. 68.72/80.94

Notation
L, F, R, BR, B, BL form a zigzag equator around the puzzle (e.g. Dark Blue, Pink, Green, Blue, Purple, Dark Green). Clustered around the north pole are UL, U, UR (Red, Yellow, Orange); and clustered around the south pole are DL, D, DR (Pale Blue, White, Brown). Rotating the puzzle is indicated in lower case within parentheses, e.g. (r) = clockwise rotation around the R face.

------------------------------------------------------------------------------------

Stage 1. Orient corners. Each case lists the corners in clockwise order around the U face from UFL to UFR, where A means the corner needs twirling anticlockwise, C means the corner needs twirling clockwise, and - means the corner is already correctly oriented. The 16 cases all have 5/81 chance of occurring, with 1/81 chance of skipping this stage.

2 corners:
[---CA] F U R U' R' F'
[C---A] (r') R U R' DR R U' R' DR'
[C-A--] F R U R' U' F'
[C--A-] (r') DR R U R' DR' R U' R'

3 corners:
[--CCC] R U R' U R U2' R'
[A--AA] R' U' R U' R' U2 R
[-C-CC] R U' R' F R' F' R or [CC-C-] R' U2' R U R' U R
[A-AA-] R' F R F' R U R' or [-AA-A] R U2 R' U' R U' R'

4 corners:
[A-CCA] F U R U' R' U R U' R' F'
[C-AAC] F R U R' U' R U R' U' F'
[CA-CA] R' U' R U' R' U R U' R' U2 R
[-ACAC] R' U R U R' U R U' R' U' R
[-CAAC] R U' R' U' R U R' U R U R'
[CA-AC] R' U R U R' U' R U' R' U' R

5 corners:
[CCCAC] R U R' U R U2' R2' U2' R U R' U R
[AAAAC] R' U' R U' R' U2 R2 U2 R' U' R U' R'

------------------------------------------------------------------------------------

Stage 2. Permute corners. The corners are numbered from 1 to 5 in clockwise order around the U face from UFL to UFR. Probabilities: F, T = 5/12 each; U = 1/12; skip stage = 1/12. (A twist of the U face to fix the corners is a "skip", even though it contributes an average of 0.8/1.2 to the turn count when it occurs.)

[3,4,5] (F1 -- Clockwise adjacent 3-cycle)
R' U2' R U R' U2 L U' R U L'

[3,5,4] (F2 -- Anti-clockwise adjacent 3-cycle)
L U' R' U L' U2' R U' R' U2 R

[2,4,5] (T1 -- Non-adjacent clockwise 3-cycle)
R' U' F' U F R (u2 r') R' DR R U' R' DR' R U

[2,5,4] (T2 -- Non-adjacent anti-clockwise 3-cycle)
(u) F U R U' R' F' (u2 r') R U' R' DR R U R' DR'

[1,3] [4,5] (U -- Unequal length pair swaps*)
(r') R U' R' DR R U R' DR' R U R' DR R U' R' DR'

* Megaminx algo from Erik Akkersdijk's website (http://erikku.er.funpic.org/rubik/).

------------------------------------------------------------------------------------

Stage 3. Lower edges. Includes fixing the orientation of moved edges - ignoring any lower edges that are correctly positioned but flipped. For this stage and the next, F is the last face. The following algorithms move an edge to R/DR. The only edges affected are R/DR, the source edge, and one other (upper) final face edge, so we can solve the lower 5 edges in any order we like. [DR/DL] means that the DR/DL edge's DR tile colour matches the R face, and its DL tile colour matches the DR face.

[DR/DL] (f') R DR U DR' U' R'
[DL/DR] (dl') U' R' DR U' DR' U R U

[DL/L] R U2 BL' U' BL U' R'
[L/DL] (r) L2 U' DR U DR' L2'

[L/U] (r) UL L DR' L DR L2' UL'
[U/L] (r) UR2' U DR' U' DR UR2

[U/R] R U DR U' DR' R'
[R/U] (dr') DR R U' DR U DR' R' DR'

[F/DR] R DR' L DR L' R'
[DR/F] DL' U' BR U' BR' U2 DL

[F/DL] R DR U' DR' U R'
[DL/F] (r) DR R2' F UR' F' UR R2 DR'

[F/L] R U' DR U DR' R'
[L/F] (f') R' DR U' DR' U R

[F/U] DR2' DL' R L' R' L DL DR2
[U/F] DR' L' R L R' DR

[F/R] U DL BR' DL BR DL2' U'
[R/F] DR' R L' R' L DR

------------------------------------------------------------------------------------

Stage 4. Permute upper edges (ignoring their orientation). The edges are numbered 1 to 5 clockwise from F/DL to F/DR. My names for the upper edge perms are Flat triangle, Tall triangle, Equal pairs, Unequal pairs, X, B, figure of eiGht, Pentagon, and Star. Probabilities: F, T, B, G = 1/6 each; E, U, X = 1/12 each; P, S = 1/30 each; skip stage = 1/60.

F1 [1,2,5] L' R2 (r') L' R' L R' (r) L
F2 [1,5,2] L' R (r') L' R L R2' (r) L

T1 [1,3,5] L' R L R'
T2 [1,5,3] R L' R' L

E [1,5] [2,3] L' R L R2' (r) L R L'

U [1,2] [3,5] L' R L R' (r) L R2' (r) L R L' R (r') L'

X [1,3] [2,5] T1 + F1

B1 [1,3,4,2,5] L' R L R' (f) R L' R' L
B2 [1,5,2,4,3] (f) L' R L R' (f') R L' R' L

G1 [1,3,2,4,5] L' R L R' (f) L' R L R'
G2 [1,5,4,2,3] (f) R L' R' L (f') R L' R' L

P1 [1,2,3,4,5] L' R L R2' (r) L R L2' (l) R L R'
P2 [1,5,4,3,2] R L' R' L2 (l') R' L' R2 (r') L' R' L

S1 [1,3,5,2,4] L' R L R' (f') L' R L R'
S2 [1,4,2,5,3] R L' R' L (f) R L' R' L

------------------------------------------------------------------------------------

Stage 5. Flip edges. This stage takes an average of 11 face turns. Sometimes a setup move is needed with the first algo. The most common situation, occurring 53.7% of the time, is 2 flipped upper edges and no flipped lower edges. It's very rare (<0.01%) to have 4 flipped lower edges, but for completeness the last algo takes care of this.

Flip F/L and F/R:
DR2' D2 DR2' U' DR2 D2' DR2 U

Flip F/L and F/DL:
DR' D2 DR2' U' DR2 D2' DR2 U DR'

Flip F/R, F/L, L/UL, and UL/UR (ring of 4 lower edges):
DL DR2' DL2' DR U2' DR' DL2 DR2 DL' U2

------------------------------------------------------------------------------------

[Edit - fixed a typo in the first Stage 3 algo.]


Last edited by Julian on Sat Oct 18, 2008 4:25 pm, edited 1 time in total.

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