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I have been making a Yoshimoto cube, using 8 cubes. I am assuming, there must be some way to create a Yoshimoto Cube consisting of 27 cubes or 64 cubes (assuming the original formula is 2x2x2). Or perhaps 16 cubes.

God knows. So, my question is. Has anyone ever tried making a Yoshimoto cube consisting of more than 8 cubes and what is the best way to go around doing it. I am lost.

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The problem is that nxnxn cubes with n odd don't have a hamiltonian cycle, which is easily proved using a checkerboard colouring. Therefore the next cube size up will the 4x4x4. Any linking of 64 cubes will easily pull apart to form a long loose loop like a necklace, so is not going to force you to restrict yourself to straightforward folding movements like the 2x2x2. It might then become quite a puzzle to fold it back together into a cube, but it won't particularly have the feel of the 2x2x2 Yoshimoto cube.

If you trust the player to restrict themselves to only standard folding moves, then there are probably interesting ways of connecting the cubes. You could start with the premise that the 4x4x4 should be able to do the normal Yoshimoto folding while keeping its 2x2x2 sub-blocks together, and see where that gets you. Maybe it could consist of two identical loops of 32 cubes.

I may come back to this question when I have more time to see if I can think of a possible design.

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