A polyhedron that can be inscribed in a sphere and whose faces are congruent regular polygons.
 There are five regular convex polygons. They are called Platonic solids.









 There are also four regular nonconvex 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: