A regular polyhedron is a three-dimensional shape whose faces
are all identical regular polygons, and whose corners are
all the same as each other. There are only five. They are
the tetrahedron, the cube, the octahedron, the dodecahedron
and icosahedron.

The ending hedron corresponds to faces and
the prefix to the number of faces. Tetra means four, dodeca
means twelve and icosa means twenty.

A regular polyhedron
is highly symmetrical, being all of edge-transitive, vertex-transitive
and face-transitive - i.e. it is transitive on its flags.