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A special class of Zonohedron. There are five parallelohedra with an infinity of equal and similarly situated replicas which are Space-Filling Polyhedra: the Cube, Elongated Dodecahedron, hexagonal Prism, Rhombic Dodecahedron, and Truncated Octahedron.

See also Parallelotope, Space-Filling Polyhedron


Coxeter, H. S. M. Regular Polytopes, 3rd ed. New York: Dover, p. 29, 1973.

© 1996-9 Eric W. Weisstein