Spherical polyhedron

In geometry, a spherical polyhedron or spherical tiling is a tiling of the sphere in which the surface is divided or partitioned by great arcs into bounded regions called spherical polygons. A polyhedron whose vertices are equidistant from its center can be conveniently studied by projecting its edges onto the sphere to obtain a corresponding spherical polyhedron.

The most familiar spherical polyhedron is the soccer ball, thought of as a spherical truncated icosahedron. The next most popular spherical polyhedron is the beach ball, thought of as a hosohedron.

Some cases of three-dimensional polyhedra are unique to spherical forms, such as hosohedra and their duals, dihedra, whose flat-faced convex analogs are degenerate. The example hexagonal beach ball, ${\displaystyle \{2,6\}}$ is a hosohedron, and ${\displaystyle \{6,2\}}$ is its dual dihedron.