is it true that the sides of regular polyhedron although having to be the same polygon, do not have to be regular polygons?
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
No, it is not true. The sides of a regular polyhedron must be the same regular polygon.
Regular polyhedra are three-dimensional geometric solids where all the faces are congruent (identical) regular polygons, and the same number of faces meet at each vertex. There are only five regular polyhedra, also known as the Platonic solids: tetrahedron, cube, octahedron, dodecahedron, and icosahedron.
In the case of a regular tetrahedron, all four faces are equilateral triangles. A cube has six square faces, an octahedron has eight equilateral triangular faces, a dodecahedron has twelve regular pentagonal faces, and an icosahedron has twenty equilateral triangular faces.
These regular polyhedra have regular polygons as faces, and all the edges and angles are congruent. So, the sides of a regular polyhedron must be regular polygons.