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Disdyakis Triacontahedron


DisdyakisTriacontahedronSolidWireframeNet

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The disdyakis triacontahedron is the dual polyhedron of the Archimedean great rhombicosidodecahedron. It is also known as the hexakis icosahedron (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_(16).

Solids inscribed in a disdyakis triacontahedron

A tetrahedron 10-compound, octahedron 5-compound, cube 5-compound, icosahedron, dodecahedron, and icosidodecahedron can be inscribed in the vertices of a disdyakis triacontahedron (E. Weisstein, Dec. 26-27, 2009).

Starting with an Archimedean great rhombicosidodecahedron of unit edge lengths, the edge lengths of the corresponding disdyakis triacontahedron are

s_1=1/(11)sqrt(1275-465sqrt(5))
(1)
s_2=3/(11)sqrt(39+(57)/(sqrt(5)))
(2)
s_3=sqrt(12-(12)/(sqrt(5))).
(3)

The corresponding midradius is

 rho=3/(22)sqrt(413+(827)/(sqrt(5))).
(4)

The surface area and volume are

S=(180)/(11)sqrt(179-24sqrt(5))
(5)
V=(180)/(11)(5+4sqrt(5)).
(6)

See also

Archimedean Dual, Archimedean Solid, Disdyakis Triacontahedral Graph

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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. 141, 2002.Wenninger, M. J. Dual Models. Cambridge, England: Cambridge University Press, pp. 25 and 27, 1983.

Cite this as:

Weisstein, Eric W. "Disdyakis Triacontahedron." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/DisdyakisTriacontahedron.html

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