Has anyone made a fully functional puzzle with cuts along (at least) the edges of a complete graph of order 6 (or more)? For example, imagine the figures below as faces of two-layer cheeses, with turning possible about every cut. Is this feasible?

-Logan

P.S.

Note that the figure on the right would lead to a bandaged two-layer cheese.

Well... regarding the left picture, I have a graph(idron) which "compliments" it:
viewtopic.php?f=15&t=18147&start=0




Joking aside, this task seems to be a very interesting one, not impossible, but difficult.




Pantazis

The one on the left is very possible. The centres for the shallow cut pieces are split in 2(4 due to 2 layer cheese) and are thus like the extensions on a 1x2x3
With the one on the right the additional cheese cuts would cut the shallow cut corners aswell, which is less desirable. So I think that is also possible, but less stable.

The one on the right could jumble if you made a 30-degree turn on one layer.

Jared: I called it bandaging in my original post, but reading the definition of jumbling on the forum, I guess that is indeed what it would do.

These sorts of puzzles can be made using the shells approach.

There are simpler puzzles which have never been made - for example, a 4- or 5-axis cheese, and the variants on those where you can slice about a horizontal plane like in the rubik's ufo, and the variants on those where the horizontal plane can only slice a multiple of two units. Those last two are actually quite complicated and interesting design challenges.