Regular polyhedra

polyhedron with regular congruent polygons as faces

Platonic solid

A dihedron (pl. dihedra) is a type of polyhedron, made of two polygon faces which share the same set of n edges. In three-dimensional Euclidean space, it is degenerate if its faces are flat, while in three-dimensional spherical space, a dihedron with flat faces can be thought of as a lens, an example of which is the fundamental domain of a lens space L(p,q). Dihedra have also been called bihedra, flat polyhedra, or doubly covered polygons.

Kepler–Poinsot polyhedron

Kepler–Poinsot polyhedron

Kepler–Poinsot polyhedron

Kepler–Poinsot polyhedron

thumb|This beach ball would be a hosohedron with 6 [[spherical lune faces, if the 2 white caps on the ends were removed and the lunes extended to meet at the poles.]]