Gear Family

I no longer have a Gear Cube. Well, I have a Gear Cube Extreme, but it is so different from the other gear puzzles I have I don't consider it part of the family. In the family are:

Gear Ball — 6 sides
Gear Tetrahedron (triangular pyramid) — 4 sides
Gear Octohedron — 8 sides
Gear Dodecahedron — 12 sides

Although they vary in the number of sides they have, they have some very important properties in common. They all have:

6 Centers (of rotation)
8 Corners (they don't all look like typical corners)
12 Edges (each "edge" has 3 parts: a cog and 2 adjoining pieces)

Thoughts on a solution:

Corners: As far as I can tell corners are ever at most only 4 moves from solved. With the Ball, Tetrahedron, and Dodecahedron it is easy to use this fact to start the solve with the corners, but with the Octahedron, whose corners are only 1 color each, it is not so clear. Scramble it, set it aside for a year or so, then try to start with the corners. It is mystifying. 

Edges: The 3 pieces that travel together are the edges. The cog is the center piece of the edge. It is possible to flip 8 edges. Do (U R) x 3. The edges in the slices between R and L, and U and D, all flip. Also all 6 centers flip. Although the edges of the Tetrahedron are a single color, if they are flipped it is obviously not solved as they jut out from the face.

The edge on the top left does not need to flip. The other two do. Talking about the 2 outer pieces of each edge, not the cog.

To do the middle layer swap thing just do R U2 R', since orientation of the gears doesn't matter yet.

Centers: The centers are the centers of rotation, not anything in the center of a pentagonal face. In my old Solutions Guide it says: "To flip the 4 centers in the vertical slice between R and L do R U F U L U B U." Think about it. (RU spin the puzzle so the front goes to the right) x 4 is another way to see it.

(R U R2 U') x 2 flips all 6 centers, which can be useful if only 2 are flipped, or all 6.

Orienting Gears: 4R or 8R or 12R or 4L or 8L or 12L or 4R' or ... If you solve it often enough you figure out how to minimize moves, but if you don't want to think about it just do R over and over until it is solved.

Okay. I just tried to solve all 4 puzzles. Ball - check. Dodecahedron - check. Tetrahedron - check. Octahedron - Fail. Things actually fell into place nicely at first. I used the centers to get the corners (the big equilateral triangle pieces) and the edges happened to be super easy. Two centers needed to flip so I did the Flip-6 algorithm then the Flip-4 algorithm, but it got locked up part way through and I got messed up and must have turned the wrong faces. It was a big mess. Here is the big problem. When I used the centers to get the corners so that all the centers and corners looked right, the edges can't just be spun into place. Nor can the middle layer swap thing fix them. They are 90 degrees off. Found a fix.

Try R U B R. If that doesn't work, try it again. That should do it. The thing is there are three different ways for the corners to look solved relative to one another, but only one of them is really correct. On the Ball, Dodecahedron, and Tetrahedron there is no question because the corners have 3 colors on them so it is obvious when they are correct. But the Octahedron corners can look right, but there is a one out of three chance they really are right. Make sense?

Gear Fun

Raymond's kiddos enjoy the Gear puzzles so I have been having fun with them too this summer. I still haven't totally relearned all of the algorithms I figured out to solve them yet, but it shouldn't be long.

Lanlan Gear Dodecahedron

My great puzzle accomplishment of late? I have finally figured out the Gear Dodecahedron. This has got to be one of the simplest puzzles ever. After thoroughly and thoughtfully scrambling it, if you just keep making random twists and turns and watch, eventually you'll notice that the 8 corners are all solved relative to one another. If you want to actually solve the corners with a little effort, you can do so in no more than 4 moves from any given scramble.

What I call the edges are the pieces that correspond to the edges of the Gear Cube. They can be positioned in ways similar to the Gear Cube, so a refresher of my old Gear Cube notes was in order.

But with the Gear Dodecahedron, the "edges" can also be flipped in a weird sort of way, but early on in my experimentation I stumbled on a simple algorithm that worked well.

The 6-cog gear pieces can be oriented correctly just like with a Gear Cube.

So what was the big challenge? What I call the centers—because they are the centers of rotation of the outer layers—can be flipped. On the Gear Cube the centers are a single color and square, so orientation does not matter. And for some reason it took me forever—well, a couple weeks or so anyway—to come up with a way, by trying different sequences, that could be used to flip centers. The sequence happens to also tweak all 12 of the 6-cog gears, as well as flipping 4 centers.

I might mention that I had pretty much lost interest in puzzling for several months. I may be back. :)