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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 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
 |  |  |
(1)
|
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(2)
|
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(3)
|
The corresponding midradius is
 |
(4)
|
The surface area and volume are
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(5)
|
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(6)
|
