MathDB

A regular polyhedron is a polyhedron that is convex and all of its faces are regular polygons. We call a regular polhedron a "Choombam" iff none of its faces are triangles. a) prove that each choombam can be inscribed in a sphere. b) Prove that faces of each choombam are polygons of at most 3 kinds. (i.e. there is a set

\{m,n,q\}

that each face of a choombam is

n

-gon or

m

-gon or

q

-gon.) c) Prove that there is only one choombam that its faces are pentagon and hexagon. (Soccer ball) http://aycu08.webshots.com/image/5367/2001362702285797426_rs.jpg d) For

n>3

, a prism that its faces are 2 regular

n

-gons and

n

squares, is a choombam. Prove that except these choombams there are finitely many choombams.

Problem Statement