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 Post subject: Crystal Pyraminx orientation
PostPosted: Thu Mar 24, 2011 6:35 pm 
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Hi all

My crystal pyraminx and latch cube and crazy 4x4 II and Trajbers octahedron and 3x3x2 arrived the other day. Needless to say I am very happy and quite scared after looking at the latch cube for a while.

Anyway, I've been working on the pyraminx and realised that (this is probably common knowledge) it seems like the corner pieces (with 3 stickers on) behave like edges and the edge pieces behave like corners. So I've now placed all of the corner pieces but the last two are not oriented correctly.

Here's my question: I don't particularly want an algorithm. I'd like to know how I go about thinking about how to orient them properly? Since I obviously want to keep all the others where they are, but orient the last two, is there a logical way to approach it? Is this what commutators are about?

To repeat: if I get desperate I'll try and find an algorithm, but I would prefer not to at this stage.

Thanks for any advice

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 Post subject: Re: Crystal Pyraminx orientation
PostPosted: Thu Mar 24, 2011 9:30 pm 
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Think of them as megaminx corners. Do you know how to solve a megaminx?

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 Post subject: Re: Crystal Pyraminx orientation
PostPosted: Thu Mar 24, 2011 10:10 pm 
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Meffert's solution to solving the Megaminx also works wonderfully on the Kilominx. I recommend getting a flowerminx and practicing on that. The Flowerminx's are still available on Mefferts. His solution basically uses two very short 4 move sequences, and I can now solve the Flowerminx, Pyraminx Crystal, and 2x2x2 cube without any help. I've even applied these same type sequences to the Pyraminx, and a hoard of other puzzles too. The technique is robust enough that it tends to work on just about any polyhedral twistypuzzle in which three rotation plains come together at a corner.
http://www.mefferts.com/puzzles/megasol1.html

The trick to the Pyraminx Crystal specifically, is to solve the corners first as a kilominx. Because each edge is shared exclusively between two non-adjacent faces, it is extremely easy to apply simple four-move three-cycles to solve the edges without affecting the corners. The megaminx corners technique will help with solving the edges intuitively as well.

Basically, you put the two mis-oriented corners on the top face. Hold the puzzle so that one of the corners faces you. Label the three adjoining faces L, R, and U.

Perform RL'R'L until the top face corner is correctly placed and oriented. You may notice some of the corners immediately below are messed up slightly. No need to worry; they will be fixed again soon. Now rotate U face without changing the orientation of the puzzle, so that the last remaining U face corner is in the front position. Perform RL'R'L again and repeat until all kilominx corners are solved! :solved:

For the edges, just remember to only rotate diagonal non-adjacent faces when performing the edge piece commutators, and you will not ruin the corners of the puzzle.

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 Post subject: Re: Crystal Pyraminx orientation
PostPosted: Sat Mar 26, 2011 1:48 am 
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Thanks for the clues.

@Ntype3, yes I have and can solve a megaminx, but I found some differences between that and the CP.

@stardust4ever, thanks for the meffert's link. I had a look and decided it was still too much information. Then I did a little more searching and came across a PDF of Jaap's solution. Basically, what I wanted from that (and gladly received) was a way to finish the last few corners. I used his simple sequences, then came back and realised they were the exact ones you gave me to fix the corners. :oops:

Anyway, I solved it! (I'm excited, anyway)

I think my method will be to solve all corners using intuition and when needed the sequence and variations you gave. Then solve all edges using the (wonderful) ultimate solution method for solving corners. (I still don't know why, but the edges and corners behave swapped, sort of). So I applied my 3x3 corner piece cycle to the CP edges and when down to the last 3, did the same setup for the end game of the ultimate solution. You can imagine my delight when I put everything back and it was done.

:D :D

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 Post subject: Re: Crystal Pyraminx orientation
PostPosted: Sat Mar 26, 2011 9:22 am 
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What you say there sounds odd. Are we talking about the pyraminx crystal, meaning 12 sided puzzle with floating edges?
Because if we do, than the corners of the puzzle behave exactly like the corners on a megaminx which behave almost exactly like those on a 3x3x3 cube. It's really funny that you thought of the corners as edges and could solve them. They really are the same as the megaminx corners. Even physically since inside you pyraminx crystal there is a megaminx and the corners of the PC are just attached to those of the megaminx. So you can just solve the corners by using corner solving algs.
The edges on the pyraminx crystal are just like edges on a normal pyraminx. That's probably why it's called like that.
So when you solve the pyraminx crystal you would just solve a kilominx, meaning megaminx corners and than cycle edges around with that plain normal but essential 4 move alg that you use when you solve a normal little pyraminx.

Edit: Oh, and when I got my first megaminx years ago I also used the Meffert's solution. However I would advise you to just solve the megaminx corners and therefore also the PC corners like a 3x3x3 cube's corners. Intuitive solving works to the last layer. At this point you can either try to figure out how you have to change the algs to make them work on the minx, what I did, or you solve orientation by the more "manual" way where you just bring a corner out, and back in its place with different orientation, than turn upper layer so another corner is moved into the old one's place and than undo all the moves you needed, so the corner that is there now gets rotated too, and all other stuff outside of the upper last layer gets restored. The same stuff can be done for placing.
You can practise that on a 3x3x3 cube. It's a really intuitive way of solving the puzzle. Once you realise what I was explaining you will end up beiing able to solve a complete 3x3x3 cube with your own "flexible" algs.
The Meffert's solution of the minx just has to many monotone and unnessecary moves.

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 Post subject: Re: Crystal Pyraminx orientation
PostPosted: Sat Mar 26, 2011 9:57 am 
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Ok I know you don't want an exact alg. But compare this scenario to the one on the 3x3x3 cube that looks exactly the same.
On a cube you would do
R2 F2 R' B' R F2 R' B R' (Assuming the cubies with the same color showing next to each other are on the right face, not the front.)

On the minx and with the shown notation the same move is
(F')2 L2 (F')2 R' F2 (L')2 (F')2 R F'

If you look at this maybe you'll get a bit of a better understanding on how you can apply the algs of the 3x3x3 to the pentagonal face geometry of the minx. You can do the same to all edge and corner orientation moves there are.


Attachments:
megaminx notation.JPG
megaminx notation.JPG [ 52.69 KiB | Viewed 1347 times ]

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 Post subject: Re: Crystal Pyraminx orientation
PostPosted: Sat Mar 26, 2011 9:07 pm 
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@alaskajoe, Thanks for the followup.

Quote:
What you say there sounds odd. Are we talking about the pyraminx crystal, meaning 12 sided puzzle with floating edges?
Because if we do, than the corners of the puzzle behave exactly like the corners on a megaminx which behave almost exactly like those on a 3x3x3 cube. It's really funny that you thought of the corners as edges and could solve them.

We are certainly talking about the pyraminx crystal, which looks like http://www.google.com.au/images?q=pyraminx+crystal. Let me explain.

On the 3x3, I learned to do it using the ultimate solution, which basically solves all edges first, using a simple 4 move sequence, and then solves all corners, using a simple 8 move sequence. The only difficult part is potentially a few setup moves before applying the last corner sequence.

The edge sequence cycles 3 edges (UF, RF and UR) around a corner (URF). The edge sequence disrupts corners. The corners sequence cycles 3 corners (ULF, ULB and URB) around the top face. The corner sequence does *not* disrupt edges (which is why the corners sequence is done last).

Anyway, when I applied the ultimate solution corner sequence to the crystal pyraminx, I discovered that it didn't move any corners at all, but rather cycled the three PC edges UF, UR and U-BL. Since none of the corners were disrupted, I concluded that since the corner sequence actually moved edges, then the edges must function as corners, and the corners must function as edges.

Also, I'm doing the same corners sequence on my megaminx now, and it isn't changing any of the corners or edges.

That was my reasoning.Anyway, the corner sequence, which definitely changes no corners but cycles 3 edges on a PC, but which cycles 3 corners on a 3x3 cube, is the following:

U, R, U', L', U, R', U', L.

If you apply that sequence to a solved 3x3 cube, and then to a solved PC, you'll see what I mean.

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 Post subject: Re: Crystal Pyraminx orientation
PostPosted: Sun Mar 27, 2011 5:16 am 
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Ha yes. I use this move to orientate corners in the last row. You CAN use that to orientate corners on a megaminx and PC though. The only thing you have to do is change it a bit. The point of the move is that after the first R turn the corner that is now BRU needs to go to BLU. So if you want to do this to a megaminx just do following:
U2, R, (U')2, L', U2, R', (U')2, L
This is the same move, only the upper face turns are two turns, thus 144° instead of only 72°

However solving orientation of 5 corners with this move is a bit more difficult. It takes some time until you know all the scenarios and how to use the move. Best here is to just try to get all corners orientated wrong first, than make it 2, than the last 3. On a 3x3x3 cube when you do the sequence once from the solved state you have 1 corner still corectly orientated. On a minx or PC you will have 2 still corectly.

Anyway you can get 3 cycles for edges on a PC by a 4 move sequence. For example just do R L R' L'
or any two faces that are "one face apart", meaning two faces that are not next to each other and also not opposite faces of the puzzle.

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 Post subject: Re: Crystal Pyraminx orientation
PostPosted: Sun Mar 27, 2011 3:58 pm 
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rline wrote:
...Also, I'm doing the same corners sequence on my megaminx now, and it isn't changing any of the corners or edges.

That was my reasoning.Anyway, the corner sequence, which definitely changes no corners but cycles 3 edges on a PC, but which cycles 3 corners on a 3x3 cube, is the following:

U, R, U', L', U, R', U', L.

If you apply that sequence to a solved 3x3 cube, and then to a solved PC, you'll see what I mean.
The question is : What are U, R and L faces on a Megaminx / any Dodecahedra? R and L on a Cube are opposite and the U turn transfers some Cubies between the faces R and L. Have a look at this Pyraminx Crystal, where I have applied the sequence U, R, U', L', U, R', U', L (where the U, R, L faces are marked with the respective letters; You are looking from above to the U face. At your right is the unchanged other part of the Pyraminx Crystal)
Image
You see that three corners have cycled as on a 3x3x3, and in addition many edges.
That's why you better do the corners first and after that the edges.
At least, I do it in this order.
Your Ultimate sequence works fine, you have just to adapt the faces :)

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 Post subject: Re: Crystal Pyraminx orientation
PostPosted: Sun Mar 27, 2011 4:30 pm 
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Yep, this is how I solve the PC two. You did the sequence correctly, I mean the way I meant it. And with that notation R L R' L' works fine to solve all PC edges after the corners are solved.

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