Hi Twisty Puzzles fans,

Polo Gear Cube was suggested by Alex Polonsky. This puzzles combines a corner+center-turning gear cube with a twisty 2x2x2.

Watch the YouTube video.
Buy the puzzle at my Shapeways Shop.
Read more at the Shapeways Forum.
Check out the photos below.

Enjoy!

Oskar

That is one awesome puzzle! Definitely my favourite from you. Hopefully I'll be able to buy myself a copy of it in the near future.

This puzzle just look's fabulous, and even more incredible the turning (from what I can see) is almost perfet .

Wow! Great job!

Fantastic puzzle, mass-production please !

I like how it retains its shape after the gear moves. I think I've got to call this one my favorite of your puzzles, too.

I uttered something that is not to be put on this forum when you twisted those corners.

AWESOME!!

Beautiful puzzle! I also like the fact that it retains its' cubic shape even after the gear moves. Another masterpiece.

Amazing!

Since the corners all turn in the same direction every time, all (!) you really need to do to solve this is get the centers fixed. Then once the centers are fixed, the corners can just be rotated until they are fixed.

A version with super stickers would probably be much, much harder.

Superb Oskar, another triumph. I think that this is the best of your gear designs. This must be mass produced.

And that's what happens when you get the perfect tolerances and outside looks O.O Amazing work ! By far my favorite from you !!

What a cool puzzle, And it seems to turn perfectly! Good job

Fantastic idea perfectly realised.
I wonder if I can resist ordering one before I hopefully can see and test it at the next DCD

...Hey Oskar, if you increased the number of teeth on the circles to 16, and similarly increased the number of teeth on the corners, could you make a "split" version that allowed 1/8 gear turns?

Cool.
For one minute I wondered why you have never implemented such gears (without the 2x2x2) before. Then I recognized that this puzzle would be trivial without the 2x2x2-moves.

Great concept and excellent execution!

With regard to your question about how many turns you'd need after a single 2x2x2 move to get it back into a state where you can just undo the 2x2x2 move... The centers cycle modulo 4 and the corners twist modulo 3 so shouldn't the LCM of 4 and 3 == 12 be the number of moves needed? Since you already did one corner twist, you'd need 11 more moves before you could undo your 2x2x2 turn.

Thinking about solving it... I can't come up with any sort of commutator-based 3-cycle for the center pieces. My gut tells me that if a 3-cycle exists, it can be in a standard commutator form.

Awesome! Great job as always Oskar.

Was thinking about a "3x3x3" version of your Gear Shift the other day...looked similar to this one. Or has that been built already?

Mass production please.

I'd really be interested to see how hard this is to solve.

I like it because it's difficulty does not coming from working out long algorithms, but from having to think far ahead before making a move.

Awesome puzzle; keep it up!

Wow, I really like this puzzle! This is really neat. Dazzling but not chaotic, exotic but somewhat familiar. I can't waiting thinking about the solving it.

Nice puzzle Oskar!!!

This is a beautiful puzzle, and I think it would be very fun to solve. It looks like it turns quite well!


Some days ago, there was a brief discussion about the difficulty of solving this puzzle in the TP chatroom. You can solve the little rectangular edge-stickers as a normal 2x2x2, and then since all corner gears must have the same amount of turning-offset from their corners, you can just make a single gear twist to fix all of the corner gears.

The tricky piece is the split center-gears, and indeed they are very difficult pieces. I came up with what I believe should be a super-long [10,14] pure 3-cycle:
X = [G, R',D',R, U', R',D,R, U, G'] (conjugates a [3,1] corner perm with a gear turn to affect only 1 piece out of the DBR and DBL corner groupings)
Y = [R',U2,R,B,U2,B', D', B,U2,B',R',U2,R, D] (a [6,1] corner orient for the previously mentioned corners)

(G = rotate corner gears 120 degrees clockwise)

I can't really comment on how short an alg would be possible for these pieces, but I think finding a nice short one wouldn't be easy! Perhaps there is another more convenient method for solving this puzzle.