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Disdyakis Dodecahedron


DisdyakisDodecahedronSolidWireframeNet

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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 W_(15).

If the original great rhombicuboctahedron has unit side lengths, then the resulting dual has edge lengths

s_1=2/7sqrt(30-3sqrt(2))
(1)
s_2=3/7sqrt(6(2+sqrt(2)))
(2)
s_3=2/7sqrt(6(10+sqrt(2))).
(3)

The inradius is

 r=3sqrt(2/(97)(15+8sqrt(2))).
(4)

Scaling the disdyakis dodecahedron so that s_1=1 gives a solid with surface area and volume

S=6/7sqrt(783+436sqrt(2))
(5)
V=1/7sqrt(3(2194+1513sqrt(2))).
(6)

See also

Archimedean Dual, Archimedean Solid, Disdyakis Dodecahedral Graph, Great Disdyakis Dodecahedron, Octahemioctahedron

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References

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.

Cite this as:

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

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