Spherical polyhedron

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

The example hexagonal beach ball, {2, 6}, is a hosohedron, and {6, 2} is its dual dihedron.

During the 10th Century, the Islamic scholar Abū al-Wafā' Būzjānī (Abu'l Wafa) studied spherical polyhedra as part of a work on the geometry needed by craftspeople and architects.

[1] The work of Buckminster Fuller on geodesic domes in the mid 20th century triggered a boom in the study of spherical polyhedra.

The best-known examples of projective polyhedra are the regular projective polyhedra, the quotients of the centrally symmetric Platonic solids, as well as two infinite classes of even dihedra and hosohedra:[5]

A familiar spherical polyhedron is the football , thought of as a spherical truncated icosahedron .
This beach ball would be a hosohedron with 6 spherical lune faces, if the 2 white caps on the ends were removed.
Tiling of the sphere by spherical triangles (icosahedron with some of its spherical triangles distorted).