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Rhombic Triacontahedron

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A Zonohedron which is the Dual Polyhedron of the Icosidodecahedron. It is composed of 30 Rhombuses joined at 32 vertices. Ede (1958) enumerates 13 basic series of stellations of the rhombic triacontahedron, the total number of which is extremely large. Messer (1995) describes 226 stellations. The intersecting edges of the Dodecahedron-Icosahedron Compound form the diagonals of 30 Rhombuses which comprise the Triacontahedron. The Cube 5-Compound has the 30 facial planes of the rhombic triacontahedron (Ball and Coxeter 1987).

See also Cube 5-Compound, Dodecahedron-Icosahedron Compound, Icosidodecahedron, Rhombic Dodecahedron, Rhombus, Zonohedron


Ball, W. W. R. and Coxeter, H. S. M. Mathematical Recreations and Essays, 13th ed. New York: Dover, p. 137, 1987.

Bulatov, V. ``Stellations of Rhombic Triacontahedron.''

Cundy, H. and Rollett, A. Mathematical Models, 3rd ed. Stradbroke, England: Tarquin Pub., p. 127, 1989.

Ede, J. D. ``Rhombic Triacontahedra.'' Math. Gazette 42, 98-100, 1958.

Messer, P. W. ``Les étoilements du rhombitricontaèdre et plus.'' Structural Topology No. 21, 25-46, 1995.

© 1996-9 Eric W. Weisstein