Disdyakis Triacontahedron (original) (raw)
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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 
.
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
The corresponding midradius is
 |
(4) |
|---|
The surface area and volume are
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