Phil Carmody wrote: >quasi writes: >> >> Prove or disprove: >> >> For each positive integer n, there are only finitely many >> convex polyhedra, up to similarity, such that all faces are >> regular polygons (not necessarily of the same type) with at >> most n edges. > >Are we to assume Euclidean geometry? I suspect with a closed >geometry, the answer would be very different.
Yes, Euclidean geometry.
The polyhedra are assumed to be in R^3.
>Then again, you'd want to exclude degenerate polyhedra even >in the Euclidean case.
Yes, assume the polyhedra are convex and non-degenerate (positive volume) with no two faces coplanar.