The octahedron being a tetratetrahedron exists inside of a sequence of symmetries of quasiregular polyhedra and tilings with vertex configurations (3.n)2, progressing from tilings with the sphere on the Euclidean plane and in to the hyperbolic airplane. The stellated rhombic dodecahedron, a compound of a few flattened octahedra used in Escher's

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