Relation To Tilings of The Projective Plane
Spherical polyhedra having at least one inversive symmetry are related to projective polyhedra (tessellations of the real projective plane) – just as the sphere has a 2-to-1 covering map of the projective plane, projective polyhedra correspond under 2-fold cover to spherical polyhedra that are symmetric under reflection through the origin. For example, the 2-fold cover of the (projective) hemi-cube is the (spherical) cube.
Read more about this topic: Spherical Polyhedron
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