A
convex polyhedron whose
faces are all identical
regular polygons, and whose
dihedral angles are all identical and whose
solid angles are all identical. Only five exist, the
tetrahedron,
cube,
octahedron,
dodecahedron, and
icosahedron. These are also called the
platonic solids.
The convexity constraint is equivalent to requiring the polyhedron be non-self-intersecting. A polyhedron which is self-intersecting but otherwise meets the constraints (except possibly for self-intersecting faces as well) is called a stellated polyhedron.