There are 5 regular polyhedra
A first step to prove that there only five regular polyhedra. The faces can only be triangles, squares or pentagons. Hexagons cannot be used as faces because in this case you would get a plane tessellation.
This picture has been used at the exhibition Simmetria, giochi di specchi - Symmetry, playing with mirrors.
© matematita
The image belongs to the sections...:
From "fun with hexagons" (From "XlaTangente")
All together (3D geometry)