The disdyakis dodecahedron is the dual polyhedron of the Archimedean great rhombicuboctahedron.
It is also called the hexakis octahedron (Unkelbach 1940; 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 .
If the original great rhombicuboctahedron
has unit side lengths, then the resulting dual has edge lengths
Holden, A. Shapes, Space, and Symmetry. New York: Columbia University Press, p. 55, 1971.Unkelbach,
H. "Die kantensymmetrischen, gleichkantigen Polyeder." Deutsche Math.5,
306-316, 1940.Wenninger, M. J. Dual
Models. Cambridge, England: Cambridge University Press, pp. 25-26, 1983.
.
gives a solid with surface
area and volume
