Blame Timur for inspiring this question.

Big cubes can be generalized into 2 groups based on their geometry: the "even" group and the "odd" group. Of course, the "even" group tends to be a little more complex.

What about Pyraminxes? If you make them larger and larger, how do you generalize them?

My instinct was to divide them into three types: the "3n" group, the "3n+1" group, and the "3n+2" group. Why? Because the 3n group has no centers, the 3n+1 group has upward-pointing centers, and the 3n+2 group has downward-pointing centers. But because I do not own and have never solved any Pyraminxes except for the regular 3-layer one, I can't figure this out easily.

Has anyone explored this sort of thing?

Nobody?

Nope. You lost me at "the odd group". All puzzles are odd to me!

I think that the method you proposed sounds like a good one. Makes sense to me, at least.

Chris

Hi Jared, I have a bit. For big cubes all of the centers are just about the same except that on odd cubes the core is exposed so you have that unique center that the even cubes don't have. Then, all of the edge wings are the same too and odd cubes have the middle edges.

Big tetrahedrons have a bit more variety in the center piece types and some more variety in the edge wing piece types too. I don't have time right now to explain it but I will follow up this weekend when I do.

Might as well bump this... it'd be nice to also see if we could get some generalized FTO stuff too, just in case anyone designs a Professor FTO or higher.