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