Polyhedron
Spherical polyhedra

When the surface of a sphere is divided by finitely many great arcs (equivalently, by planes passing through the center of the sphere), the result is called a spherical polyhedron. Many convex polytopes having some degree of symmetry (for example, all the Platonic solids) can be projected onto the surface of a concentric sphere to produce a spherical polyhedron. However, the reverse process is not always possible; some spherical polyhedra (such as the hosohedra) have no flat-faced analogue.
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