Regular polyhedra (other)

Besides the five Platonic solids (the regular convex polyhedra), there are other types of regular polyhedra if we relax some conditions. These include the Kepler–Poinsot polyhedra, which are regular but non-convex. They have regular faces and the same number of faces meeting at each vertex, but their faces or vertices may intersect themselves.

Important properties

• Kepler–Poinsot polyhedra are non-convex regular polyhedra.

• There are exactly four Kepler–Poinsot polyhedra: the small stellated dodecahedron, great dodecahedron, great icosahedron, and great stellated dodecahedron.

• All faces are regular polygons, and the same number of faces meet at each vertex.

• These polyhedra can have star-shaped faces or intersecting edges.