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Hosohedron
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In spherical geometry, an n-gonal hosohedron is a tessellation of lunes on a spherical surface, such that each lune shares the same two polar opposite vertices.
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
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.
Platonic solid
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In geometry, a Platonic solid is a convex, regular polyhedron in three-dimensional Euclidean space. Being a regular polyhedron means that the faces are congruent regular polygons, and the same number of faces meet at each vertex. There are only five such polyhedra:
Kepler's Platonic solid model of the Solar System from Mysterium Cosmographicum (1596)
Kepler's Platonic solid model of the Solar System from Mysterium Cosmographicum (1596)
Icosahedron as a part of Spinoza monument in Amsterdam
Icosahedron as a part of Spinoza monument in Amsterdam
A set of polyhedral dice.
A set of polyhedral dice.
Image: Kepler Hexahedron Earth
Image: Kepler Hexahedron Earth