Regular Polyhedron

• There are five regular convex polygons. They are called Platonic solids.

A regular tetrahedron has 4 vertices, 6 edges and 4 faces:
A regular hexahedron has 6 vertices, 12 edges and 8 faces:
A regular octahedron has 6 vertices, 12 edges and 8 faces:
A regular dodecahedron has 20 vertices, 30 edges and 12 faces:
A regular icosahedron has 12 vertices, 30 edges and 20 faces:

• There are also four regular non-convex polyhedra, which are called regular star polyhedra.
  They are the small stellated dodecahedron, the great stellated dodecahedron, the great dodecahedron and the great icosahedron.This is a small stellated dodecahedron; it is made up of 60 congruent triangles. It was discovered by Kepler in 1619:

A sculpture of a small stellated dodecahedron stands in the district of Bouzaréah in Algiers: