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Deltoidal Hexecontahedron


DeltoidalHexecontahedronSolidWireframeNet

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The deltoidal hexecontahedron is the 60-faced dual polyhedron of the small rhombicosidodecahedron. It is sometimes also called the trapezoidal hexecontahedron (Holden 1971, p. 55), strombic hexecontahedron, or dyakis hexecontahedron (Unkelbach 1940). It is illustrated above together with a wireframe version and a net that can be used for its construction.

It is Wenninger dual W_(14).

Deltoidal hexecontahedron hullsDeltoidalHexecontahedronHulls

A tetrahedron 10-compound, octahedron 5-compound, cube 5-compound, icosahedron, dodecahedron, and icosidodecahedron can all be inscribed in the vertices of the deltoidal hexecontahedron (E. W. Weisstein, Dec. 24-27, 2009). The resulting compound of all these inscriptable solids is also illustrated above.

Starting from a small rhombicosidodecahedron of unit edge length, the edge lengths of the corresponding deltoidal hexecontahedron are

s_1=1/(11)sqrt(5(85-31sqrt(5)))
(1)
s_2=1/3sqrt(25-5sqrt(5)).
(2)

The corresponding midradius is

 rho=1/(22)sqrt(5(283+79sqrt(5))).
(3)

The surface area and volume are

S=(100)/(11)sqrt(79-16sqrt(5))
(4)
V=(100)/(33)(5+4sqrt(5)).
(5)

See also

Archimedean Dual, Archimedean Solid, Deltoidal Hexecontahedral Graph, Hexecontahedron, Small Rhombicosidodecahedron

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References

Holden, A. Shapes, Space, and Symmetry. New York: Columbia University Press, p. 55, 1971.Kabai, S. Mathematical Graphics I: Lessons in Computer Graphics Using Mathematica. Püspökladány, Hungary: Uniconstant, p. 139, 2002.Unkelbach, H. "Die kantensymmetrischen, gleichkantigen Polyeder." Deutsche Math. 5, 306-316, 1940.Wenninger, M. J. Dual Models. Cambridge, England: Cambridge University Press, p. 24, 1983.

Cite this as:

Weisstein, Eric W. "Deltoidal Hexecontahedron." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/DeltoidalHexecontahedron.html

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