OK so I think all the pieces are the same shape? That is counterintiutive to me, and very cool. I guess its a side effect of making the sides have an even number of fingers.
This ought to work for any regular polyhedron I suspect, and maybe for all completely convex polyhedra even at higher complexity. Concave shapes would work but be hard to keep aligned maybe? Have you fooled with any other shapes?
Yes, all the sides are the same shape, an equilateral triangle. I haven’t played with it to create other shapes but it would probably work for those that have a triangular side. A d6 would he made up of squares, a d8 of diamonds etc.
No, d8s are also equilateral. You could take 4 faces from the d20 and make a d4, take 8 more and make a d8, without designing a single extra thing.
Make regular pentagons, and you’ve got a d12.
Make “kites” and you’ve got your d10 [Technically, a “pentagonal trapezohedron”], change the numbers to be 10-00 and you have your percent die, and voila, a full 7-set of D&D dice.