Tessellation Polyhedra

Abstract

Gen Among the infinitely many convex polyhedra that exist, there are some whose faces are all regular polygons. They are called “regular faced polyhedra” (RFP for short). Can you guess how many such polyhedra there are?

Kyu Hmm… Are they only the Platonic solids and the Archimedean solids? Or are there more?

Gen First of all, we will take into consideration two groups of simple polyhedra for RFPs: one is the group of regular n-gonal prisms, and the other is the group of regular n-gonal antiprisms. Regular n-gonal prisms have regular n-gons as their top and bottom faces, and their side faces are all identical squares. Regular n-gonal antiprisms have regular n-gons as their top and bottom faces and their side faces are identical equilateral triangles. There are infinitely many of both kinds.