is it true that the sides of regular polyhedron although having to be the same polygon, do not have to be regular polygons?

Answer 1

A regular polyhedron needs all the symmetries! In fact, the Wiki definition of a regular polyhedron is:
"A regular polyhedron is a polyhedron whose faces are congruent regular polygons"
Read up the very interesting Wiki article:
http://en.wikipedia.org/wiki/Regular_polyhedron