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 Post subject: Solving Problems with the Vulcano
PostPosted: Wed Dec 22, 2010 6:11 am 
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Hello people,

I have a problem with solving the vulcano. How do you solve a three cycle on a babyface of the pyraminx ? It's a three cycle of (edge babyface) pieces. Thanks!

- Greg :)

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 Post subject: Re: Solving Problems with the Vulcano
PostPosted: Wed Dec 22, 2010 6:15 am 
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See if you can pair up the Babyface edges to other babyface edges that they should line up with when solved. Then try and solve it that way. Maybe the use of R' L R L' maybe able to work with pairing one edge at a time.

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 Post subject: Re: Solving Problems with the Vulcano
PostPosted: Wed Dec 22, 2010 6:33 am 
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Yeah I tired that just before you posted ;) It works!! Thanks though!

- Greg

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 Post subject: Re: Solving Problems with the Vulcano
PostPosted: Wed Dec 22, 2010 5:37 pm 
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My solving strategy is to solve the entire bottom face (I always pick green) using intuition. This is quite easy. I first place the 3 big triangles and then I drop in place the 3 small triangles with a simple (1, 1) commutator. About 15 moves total.

I then solve the rest of the large triangles on all of the faces. This is really just intuition and takes another ~8 moves.

I then solve all of tips using intuition, and sometimes a (1, 1) commutator. Another 20-24 moves.

At this point the only thing that is left is the small triangles on the remaining 3 faces. I solve 1-2 at a time using a simple 3-cycle which is just a (3, 1) commutator. This commutator is simple enough that it feel like intuition. Use Gelatinbrain to play with any of the larger tetrahedra and you should be able to find it easily. Using either it, its reverse, mirror, or mirrored reverse all of the small triangles can be solved with no more than 1 setup move. This whole step takes about 40-50 moves.

So overall this strategy is 100 moves or less.

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 Post subject: Re: Solving Problems with the Vulcano
PostPosted: Wed Dec 22, 2010 5:52 pm 
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My method:

Putting the bg triangles in place: about 15-20 moves max
Attaching mini corners to their corresponding big triangles: about 20 moves
Making correct pyraminx edge for the top corner with three cycles (i do face last): about 30 moves
Making the last face edges about 20 moves

85-90 move solution

- Greg :D

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 Post subject: Re: Solving Problems with the Vulcano
PostPosted: Wed Dec 22, 2010 6:49 pm 
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RubixFreakGreg wrote:
My method:

Putting the bg triangles in place: about 15-20 moves max
Attaching mini corners to their corresponding big triangles: about 20 moves
Making correct pyraminx edge for the top corner with three cycles (i do face last): about 30 moves
Making the last face edges about 20 moves

85-90 move solution

- Greg :D

For what it's worth, the Vulcano/Trignis is equivalent to Gelatinbrain's 5.1.13 with the outer cage of edges removed. Since you can't see the internal stickers on 5.1.13 you can't perfectly simulate a Vulcano solve but I just solved the inner 4 faces on 5.1.13 in 46 moves. I think if you try to be efficient on the Vulcano you can solve it in 60-70 moves.

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 Post subject: Re: Solving Problems with the Vulcano
PostPosted: Sun Dec 26, 2010 1:24 pm 
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I was trying to pair up the 6 sets of edges for the last step. I'm down to the last 2 sets. Does anyone know how to pair up the last 2? Algorithms? :?


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 Post subject: Re: Solving Problems with the Vulcano
PostPosted: Sun Dec 26, 2010 1:41 pm 
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Flipping the pair over is really useful. Don't worry if you interchange the other solved pairs of edges, because it'll become a pyraminx solve.

Flip the right pairs of edges in the right places, while using the F turn, and that should solve it

If you want algorithms & step-by-step, pm me, but I don't want to ruin it for you if you just want a bit of help.

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 Post subject: Re: Solving Problems with the Vulcano
PostPosted: Sun Dec 26, 2010 3:02 pm 
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Here's my situation NType3. The left edges are orange/green on top and yellow/orange on bottom. On the right there's yellow/orange on top and orange/green on bottom. Sending you a pm.

Just need to pair those last 2 sets up.


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 Post subject: Re: Solving Problems with the Vulcano
PostPosted: Sun Dec 26, 2010 10:10 pm 
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Anyone know the parity algorithm-after you pair up edges and you try to solve like a pyraminx and end up with two switched edges?


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 Post subject: Re: Solving Problems with the Vulcano
PostPosted: Mon Dec 27, 2010 12:01 am 
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77mouser wrote:
Anyone know the parity algorithm-after you pair up edges and you try to solve like a pyraminx and end up with two switched edges?

Ugh... I absolutely hate this situation; there are 2 ways of dealing with it, rotating one of the "baby" faces and acting as if that is the only correct face and resolve to whole thing or use a preemptive approach, solving the "trivial" tips first then solving the rest of the puzzle based on the corners; it seems stupid, but after several solves using this approach I have yet to be met with this parity. Monopoly knows of an actual alg for this, but I believe my methodology of solving it would be easier.

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 Post subject: Re: Solving Problems with the Vulcano
PostPosted: Mon Dec 27, 2010 11:53 pm 
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MonkeyZ wrote:
77mouser wrote:
Anyone know the parity algorithm-after you pair up edges and you try to solve like a pyraminx and end up with two switched edges?

Ugh... I absolutely hate this situation; there are 2 ways of dealing with it, rotating one of the "baby" faces and acting as if that is the only correct face and resolve to whole thing or use a preemptive approach, solving the "trivial" tips first then solving the rest of the puzzle based on the corners; it seems stupid, but after several solves using this approach I have yet to be met with this parity. Monopoly knows of an actual alg for this, but I believe my methodology of solving it would be easier.

Your "preemptive" approach will work and is a good idea. I don't believe turning one "baby face" and then solving to that will work though unless you also break up the already paired edges. The reason is that the small edge pieces always remain in an even-cycle even though you can pair them up in such a way that new paired edge piece groups are in an odd cycle. Turning a baby face and re-solving to that doesn't change the parity of either the individual edge pieces or the edge pair groups. You have to break up and re-form the groups to resolve the odd cycle of the paired groups.

It turns out that the shortest pure commutator-based 3-cycle of the individual edge pieces (or big triangles) on this puzzle is 8 moves. Also, edge pair parities require two 3-cycles to resolve. Here is the shortest sequence (22 moves) I could come up with to solve this parity pure:

/* You can paste this sequence into Gelatinbrain's 5.1.13 puzzle to see it in action. */
/* Setup first 3-cycle */
[A, D&2],
/* Do cycle -- (1,3) */
[ACB&2], [CAD&2, D'&2, CAD'&2], [ACB'&2], [CAD&2, D&2, ADC'&2],
/* Undo setups */
[D'&2, A'],
/* Setup second cycle */
[B'],
/* Second cycle (3,1) */
[CAD&2, D'&2, CAD'&2], [ACB&2], [CAD&2, D&2, ADC'&2], [CBA'&2],
/* Undo setup */
[B]


Note that the only way this whole routine can be shorted is by using other 3-cycles don't need as many setup moves. I think 18 moves is a reasonable goal.

For very small puzzles such as the Vulcano I think reduction is a net-loss. Efficient cycling of individual pieces should win out in the average case.

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 Post subject: Re: Solving Problems with the Vulcano
PostPosted: Tue Dec 28, 2010 8:26 am 
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Got it solved! I used 2 somewhat short 3-cycles of edges to fix the parity. Thanks for the help. :D


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 Post subject: Re: Solving Problems with the Vulcano
PostPosted: Wed Jan 05, 2011 4:13 pm 
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Hopefully this isn't too late since this topic's last post to be considered a bump. I have a parity situation.
I have tried almost everything. Please help. I hope you can understand my picture. :oops:


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 Post subject: Re: Solving Problems with the Vulcano
PostPosted: Wed Jan 05, 2011 4:27 pm 
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Are all other edge pair solved?
If so... If we call the top tip T (nevermind the 'trivial' tips), and the green side (just the extended face) R, then...

R T R' T R T R' T

You might have to do it twice.

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 Post subject: Re: Solving Problems with the Vulcano
PostPosted: Wed Jan 05, 2011 4:29 pm 
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I don't know how this can be easily explained but I will try:
First you bring in a correctly paired edge from the bottom layer by twisting a pyraminx vertex. Then, you perform the 2-edge flip on that edge and ONE of the incorrect edges, so that one piece falls into the correct place. Now, turn the faces so that the 2 out-of-place edges are paired, bring up the edge-pair that you destroyed the orientation of earlier and perform the 2-edge flip again.
puzzle solved :D
For this specific case, do a F turn on the yellow face, bring up the correctly solved blue-green edge, perform a 2-edge flip, turn the yellow face back by F", and perform the 2-edge flip again.

Hope I helped!
-sj

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 Post subject: Re: Solving Problems with the Vulcano
PostPosted: Wed Jan 05, 2011 5:20 pm 
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Er, what's the algorithm for the 2 edge flip? :oops:

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 Post subject: Re: Solving Problems with the Vulcano
PostPosted: Wed Jan 05, 2011 5:26 pm 
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Staring at the face with both edges on the top two slots, where upper vertex - U, left vertex = L and right vertex = R:
R' U L' U' L R

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 Post subject: Re: Solving Problems with the Vulcano
PostPosted: Wed Jan 05, 2011 5:52 pm 
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Thanks Monopoly and Steveo too! Those algorithms were very helpful! Now solved! :solved: :D

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 Post subject: Re: Solving Problems with the Vulcano
PostPosted: Tue Jan 18, 2011 1:43 pm 
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So HAS anyone come up with a "clean" algorithm for, say, a three cycle of the baby face edges yet. I"m so close to solving this puzzle on my own, but I'm stuck at the edges. My approach so far is corners, centers - and then I wanted to pair up edges and then solve like a pyraminx - basically a reduction method. It just seems so intuitive that way, but I can't move the edges around without messing up the "centers" and it's driving me crazy! :)

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 Post subject: Re: Solving Problems with the Vulcano
PostPosted: Tue Jan 18, 2011 1:46 pm 
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What I would do is this (you'll have to see for yourself to see what happens): I use two algorithms for pairing edges. Smaller R is a babyface move.

R' L R L' r L R' L' R r' or L R' L' R l' R' L R L' l.

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 Post subject: Re: Solving Problems with the Vulcano
PostPosted: Tue Jan 18, 2011 1:57 pm 
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SEBUVER wrote:
What I would do is this (you'll have to see for yourself to see what happens): I use two algorithms for pairing edges. Smaller R is a babyface move.

R' L R L' r L R' L' R r' or L R' L' R l' R' L R L' l.


I will try that, and forgive my ignorance here - Capital letters are a vertex turn (like a regular pyraminx turn?). And then lower case letters would mean a "face" turn? If so, then which way are you looking at the puzzle to make r and l? Sorry if this is answered above, I'm on medicine and I'm confused! :)

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 Post subject: Re: Solving Problems with the Vulcano
PostPosted: Tue Jan 18, 2011 2:00 pm 
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That's okay. If you hold the puzzle so one face faces you, the Ls and Rs are the corners at the bottom of the puzzle. However, if you hold the puzzle like that, there is a front, a right, a left and a down face.

l is opposite from R
r is opposite from L.

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 Post subject: My Vulcano solution
PostPosted: Tue Jan 18, 2011 4:09 pm 
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Wile we are on the topic of Vulcano solving, I have worked out a wonderful strategy for solving it. I was going to get around to posting this, but the topic rather got started without me while I procrastinated.

Step #1: Match the tips!

Rather than start with a face, I start with a corner. But first things first, the tips are the easiest thing to straiten out, as it only requires rotating the faces and tips without disrupting the meat of the puzzle. The tips can just as easily be the last thing you solve as it is the first, but I recommend matching all of the corner tips first, as this cuts down on the visual clutter and helps to quickly identify the centers when they are already lined up. There are some extremely simple three piece commuters that you should be able to do. Find a tip that belongs on a corner on an adjacent face. Rotate the corner tip first so that the piece you want to replace is in the triangular face plane (this is important not to mess up what you've already got if one of them is solved). Rotate the big triangle face around so that the tip is on the correct corner, and twist it into it's proper place. When you get to a point at which there are only three tips left that are out of place, simply manipulate the Vulcano so that all three are on the same corner (you can use slice moves to do this if you want as everything else is already messed up so it doesn't matter). Simply twist the last corner tip and it they will fall into place.

Step #2: Solve the first corner.

This step is rather intuitive. You basically just pick a corner and find three center pieces that go in that corner. Find the two edge wings that match one of the center corners and line them up to complete a small triangle. Complete two more small triangles that match your first triangle. You'll know they match because all three tips will have the same three colors. When you are done, you should now have completed an entire corner of the Vulcano right down to the center cut line.

Step #3: Pair the edges.


As tempting as it be to go ahead and start pairing the other corners, don't do it. The edge pairing is the most difficult stage of the Vulcano solve, due to some nasty parity issues that I still haven't figured out how to deal with completly. Turn the Vulcano over so that the newly solved corner is on the bottom. Nothing we do from here on out is going to disturb the bottom corner. Rotate the Vulcano so that the solved corner is Down, the unsolved face is Up, and one of the corners on the Up face is pointing towards your face. This is the Front corner, F. The "R" and "L" corners are located in the back of the puzzle. I only use two classic Pyraminx algorithms in my solution, utilising the "R" and "L" corners. Additionally, the only non-pyraminx move you will use from here out is the "U" face rotation. The first Pyraminx algorithm you will need to know is a four move 3-edge shuffle:

3-Edge Shuffle: (R+, L-, R-, L+)
If you have access to a regular Pyraminx, it would be a good idea to practice this move a bit.

This simply swaps the three Pyraminx edges on the top row, flipping two of them in the process. Repeated three times, it will result in the same configuration. Note the colors of the edge pieces in the directly adjacent to the top layer. There is a lower deck and an upper deck within the top layer. Each edge piece has two colors. Check to see if any of the three pieces on the bottom set have matching colors. If so, then use the 3-edge shuffle to mix them up. This manuver flips two Pyraminx edges during the rotation, switching two sets of paired pieces between the upper and lower decks. Now check to see if there are three unique color combinations on each deck. If so, then rotate the U face to try to align the edge pairs. One of two things will happen: Either all three edges will be paired properly, or you will have one of two parity situations. The first parity situation occurs when one of the edges is is paired but the other two are wrong colors. Rotating the Up face around to different positions will always match match one of the edges, leaving the other two messed up. If that is the case, then do the 3-edge shuffle, now you should be able to rotate the Up face to a position so that none of the edges are paired. While this may seem counterintuitive to your goal, it means that you can perform the shuffle manuver again, either once or twice, until all of the pieces in the upper or lower respective decks have different color combinations. This time, however, since none of the edge pieces are currently paired, a simple U face rotation will simultaneously pair all three!

However, step #3 is not over yet. There is a 50-50% chance that you may have encountered parity error #2. Check the position of the three newly paired edges. Find an edge that is in proper orientation (there is either 1 correctly oriented or all three of them), and rotate the entire Down corner so that it matches with the edge color. The other two edges will either have the Up-face color facing up (proper orientation for both) or sideways (flipped). Check to make sure that the non-Up-face color of the edge matches the side it's next to. If not for example, the Down corner is Green-Blue-Yellow and the Up face is Orange, and the Blue Up-face edge is correct, but the Yellow and Green edges need to be switched, then you have the dreaded Parity #2. and the edges cannot be solved as Pyraminx edges. What I do in this case is a 3-edge shuffle, followed by U+ or U- (?), then another 3-Edge Shuffle, at which point I restart step 3, and hopefully next time the Parity does not occur again. While I don't know for sure how to properly address it, I do know that both Parities can be fixed using by only using the 3-edge shuffle combined with U turns. :?

However, if you got lucky and did not recieve a Parity 2 error, then the edges will either be all properly aligned, positioned, and oriented, or two of them will need flippage. Orient the Vulcano so that the two edges that need flipping are placed at the LR and FL edges. Do the 3-edge shuffle, fololowed by a rotation of the entire puzzle120 degrees clockwise. Now do another 3-edge shuffle, rotate the whole puzzle 120 degrees counterclockwise, do the 3-piece shuffle one more time, and the Pyraminx edges will be solved. Whew, that was a lu-lu... :roll:

Flip FL and LR edges:
(R+, L-, R-, L+), whole puzzle 120 degrees clockwise on the U axis,
(R+, L-, R-, L+), whole puzzle 120 degrees counterclockwise,
(R+, L-, R-, L+)


Step 4: Solve the final nine top layer corners.
You are almost done. There is one more Pyraminx algorithm that you will need to practice:

The R corner twiirl (clockwise) 8 moves:
(R+, L-, R+, L+, R+, L-, R+, L+)

Practice this algorithm on a Pyraminx. If you mess this rythmic easy-to-remember algorithm up, then it's back to Step 3 all over again! Didn't think you want to do that. This algorithm rotates a central corner while leaving the everything else untouched. It is really quite simple. It starts off the same as the 3-piece shuffle, but You twist the R face clockwise (+) every time, while the L face alternates between counter clockwise and clockwise (- and +). You can also make the opposite manuver by rotating the R face backwards. If you twist R clockwise, the corner twirls clockwise, and visa-versa. The L face alternates with each turn, while the right face goes one direction only. Using only the corner twirl algorithm and rotations of the U face, you can position a center tip into the appropriate corner and use the twirl algorithm to put it into place. If one of the centers on your target corner is already in place, it's a good idea to twirl the corner down first sothe target position is up. Then just U-turn and twirl the corner back. Now you can focus on the U face and the other corners. If you get the last three center/tips that need aligning together on the same corner, then one more application of the twirl algorithm will solve itself.

:solved: Congrats, you have solved the Vulcano! :solved:

Sorry if my method is unclear and hard to follow, but I taught myself the Pyraminx as a child, and I have self-taught myself the Vulcano using only two simple Pyraminx algorithms combined with U turns, the rest is intuition!!!


Attachments:
pyraminx vulcano notation.png
pyraminx vulcano notation.png [ 15.33 KiB | Viewed 3447 times ]

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 Post subject: Re: Solving Problems with the Vulcano
PostPosted: Tue Jan 18, 2011 4:57 pm 
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This is the method I use:
1. Match the tips and the corners (regardless of the position).
2. Solve the corners (intuitive and straightforward).
3. Pair 3 edges intuitively. Pair the rest 3 by a simple 6-moves algo. Pyraminx is ready.
4. Solve the Pyraminx. If it can not be solved (edge parity), cycle 3 corners and repeat ii. 2-4.

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 Post subject: Re: Solving Problems with the Vulcano
PostPosted: Tue Jan 18, 2011 5:06 pm 
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To solve, I just do intuition, solving any face completely, then solving a second face completely, the solving the large triangles of the remaining faces, then the tips, then doing a 15-move algorithm to permutate the baby face edges.

I don't know the "correct" terminology, but to cycle the three edges, I face the puzzle towards me so the baby face I want to cycle the edges of is on top, with a vertex to the left, right, bottom, and away. I do [R', U', R, U', R', U', R], U, [same as first].

Fun puzzle to solve, very smooth action and overall a great design!

Chris

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 Post subject: Re: Solving Problems with the Vulcano
PostPosted: Tue Jan 18, 2011 10:06 pm 
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SEBUVER wrote:
What I would do is this (you'll have to see for yourself to see what happens): I use two algorithms for pairing edges. Smaller R is a babyface move.

R' L R L' r L R' L' R r' or L R' L' R l' R' L R L' l.


Yay - using this I was able to finish the puzzle. Now that I see what it does, I'm mad at myself for not figuring that one out! At any rate, my solution goes like this now:

Tips: Intuitively
Centers" Intuitively
Pair up edges using algorithm above and put into place using pyraminx moves.
Fix any edge "parity" using three cycles (alg listed above)

Works for me! Thanks for the help!

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 Post subject: Re: Solving Problems with the Vulcano
PostPosted: Tue Jan 18, 2011 10:16 pm 
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Here's my parity fix algorithm. I think it's pretty simple and it makes sense to me.

Hold the cube with a flat side up. U = baby face; L,R,D = corner turns
This move will swap+flip the UF and U(back)R edges.

U (R' D R) (L D L')
Rotate entire cube like U
U (R' D R) (L D L')
U

From here it's just a simple Sune if you setup the pieces right.
L D L' D L D L' D'

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 Post subject: Re: Solving Problems with the Vulcano
PostPosted: Tue Jan 25, 2011 5:22 pm 
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I've solved this once, and every time since then I come across this problem. Does this happen on a regular pyraminx? I;ve never encountered it on one... Everything else is solved but these two edges which are paired. Any help would be appreciated. Thanks


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 Post subject: Re: Solving Problems with the Vulcano
PostPosted: Tue Jan 25, 2011 5:43 pm 
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I have the same problem.

I have scambled and solved this puzzle atleast 10 times; I get this "parity" error EVERY time!
this makes me thing that I am failing to create a true random scramble.

I solve with this order
1. centers/large triangles
2. tips
3. edges

I have also tried doing edges as step 2, then tips as step 3, but have the same results.


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 Post subject: Re: Solving Problems with the Vulcano
PostPosted: Tue Jan 25, 2011 6:26 pm 
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christian b wrote:
I've solved this once, and every time since then I come across this problem. Does this happen on a regular pyraminx? I;ve never encountered it on one... Everything else is solved but these two edges which are paired. Any help would be appreciated. Thanks

This is not possible on a regular pyraminx. The reason of this is that your corners were arranged around "wrong" core corners. Just try to visually keep the same position of the core and make a cycle shift of any of your 3 corners around.

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 Post subject: Re: Solving Problems with the Vulcano
PostPosted: Tue Jan 25, 2011 8:44 pm 
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Timur wrote:
christian b wrote:
[...]Everything else is solved but these two edges which are paired. Any help would be appreciated. Thanks
This is not possible on a regular pyraminx. The reason of this is that your corners were arranged around "wrong" core corners. Just try to visually keep the same position of the core and make a cycle shift of any of your 3 corners around.

Hi Timur, can you elaborate on what you mean? I think you might have an alternate way to think about this parity. If you scroll up you can read my explanation and fix or GuiltyBystander's fix.

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 Post subject: Re: Solving Problems with the Vulcano
PostPosted: Tue Jan 25, 2011 8:45 pm 
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I posted my tutorial on my channel (link) and hopefully it helps a bit.

There's only one error I made with the 3-cycle, and that's that I forgot the counterclockwise cycle :oops: so you may have to do the 3-cycle twice :|

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 Post subject: Re: Solving Problems with the Vulcano
PostPosted: Tue Jan 25, 2011 10:25 pm 
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NType3 wrote:
I posted my tutorial on my channel (link) and hopefully it helps a bit.

There's only one error I made with the 3-cycle, and that's that I forgot the counterclockwise cycle :oops: so you may have to do the 3-cycle twice :|
I made a video response to the end of your video with your 18-move 3-cycle. It's just 2 setup moves, a 8-move 3-cycle and then undo setups (12 moves total). I created another video with just the 3-cycle and no setups but Youtube is taking a long time to process the video. I will update the description with a link when Youtube finishes.

I think sticking to one short 3-cycle and just using setup/undo moves is much easier than any other suggested method I have seen. No special cases.

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 Post subject: Re: Solving Problems with the Vulcano
PostPosted: Tue Jan 25, 2011 11:07 pm 
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I'll annotate a link to it

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 Post subject: Re: Solving Problems with the Vulcano
PostPosted: Wed Jan 26, 2011 4:13 am 
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bmenrigh wrote:
Hi Timur, can you elaborate on what you mean? I think you might have an alternate way to think about this parity. If you scroll up you can read my explanation and fix or GuiltyBystander's fix.

Imagine that the screw caps also have stickers (that are normally hidden). If you solve the corners according to these stickers, you will not get the parity, because all corners will be at "right" places. But if only one corner is at its right position, the others being shifted, the parity arises.
So, resolving the parity is finding another corners location. So far, only one cycling movement always helped me, this makes me think that the good and bad parity ratio is 50/50. This consideration leads to a strange thing that contradicts my first paragraph - if you make 3 shifts and all the corners return to their original position, you switch the parity situation. Have to try it :)

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 Post subject: Re: Solving Problems with the Vulcano
PostPosted: Wed Jan 26, 2011 5:15 am 
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I understand what you mean here:

Timur wrote:
Imagine that the screw caps also have stickers (that are normally hidden). If you solve the corners according to these stickers, you will not get the parity, because all corners will be at "right" places. But if only one corner is at its right position, the others being shifted, the parity arises.
So, resolving the parity is finding another corners location. So far, only one cycling movement always helped me, this makes me think that the good and bad parity ratio is 50/50. This consideration leads to a strange thing that contradicts my first paragraph - if you make 3 shifts and all the corners return to their original position, you switch the parity situation. Have to try it :)


but I believe that you can fix this "Parity" with a combination of 2 Edge 3-cycles. I made a video of it, and it is uploading now. here it is!

-Mark- :)

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