Spherical polyhedron

A spherical polyhedron is a type of non-Euclidean polyhedron that is a tiling of the sphere where all edges are great arcs. Usually it is implied that the faces are convex, and no self-intersection is allowed.

The regular spherical polyhedra are spherical projections of the Platonic solids, the regular hosohedra, and the regular dihedra. Hosohedra and dihedra are degenerate in Euclidean space but perfectly valid for spherical polyhedra.