Deltoidal Icositetrahedron


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The deltoidal icositetrahedron is the 24-faced dual polyhedron of the small rhombicuboctahedron. It is also called the trapezoidal icositetrahedron (Holden 1971, p. 55). It is illustrated above together with a wireframe version and a net that can be used for its construction.

It is Wenninger dual W_(13)

A deltoidal icositetrahedron appears in the middle right as one of the polyhedral "stars" in M. C. Escher's 1948 wood engraving "Stars" (Forty 2003, Plate 43).

Deltoidal icositetrahedron inscribed solidsDeltoidalIcositetrahedronHulls

A stella octangula, attractive octahedron 4-compound (whose dual is an attractive cube 4-compound), and cube can all be inscribed in a deltoidal icositetrahedron (E. Weisstein, Dec. 24, 2009). Superposing all these solids gives the beautiful compound illustrated above.

For a small rhombicuboctahedron with unit edge length, the deltoidal icositetrahedron has edge lengths


and inradius


Normalizing so the smallest edge has unit edge length s_1=1 gives a deltoidal icositetrahedron with surface area and volume


See also

Archimedean Solid, Deltoidal Icositetrahedral Graph, Deltoidal Icositetrahedron Stellations, Icositetrahedron, Octahedron 4-Compound, Small Rhombicuboctahedron, Stella Octangula

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Escher, M. C. "Stars." Wood engraving. 1948., S. M.C. Escher. Cobham, England: TAJ Books, 2003.Holden, A. Shapes, Space, and Symmetry. New York: Columbia University Press, p. 55, 1971.Wenninger, M. J. Dual Models. Cambridge, England: Cambridge University Press, p. 23, 1983.

Cite this as:

Weisstein, Eric W. "Deltoidal Icositetrahedron." From MathWorld--A Wolfram Web Resource.

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