Octahedron 20-Compound


A first compound of 20 octahedra can be constructed from the vertices of icositruncated dodecadodecahedron uniform polyhedron and a second from the vertices of the great dirhombicosidodecahedron or great snub dodecicosidodecahedron (E. Weisstein, Aug. 29-30, 2023). They are duals of corresponding cube 20-compounds, the second of which is noted and depicted by Wenninger (1982, pp. 139-140).

The skeleton of the first compound is 20K_(2,2,2) (where K_(2,2,2) is isomorphic to the octaherdal graph) and of the second compound is the great dirhombicosidodecahedral graph.

Both are implemented in the Wolfram Language as PolyhedronData[{"OctahedronTwentyCompound", n}] for n=1 and 2.


These octahedron 20-compounds are illustrated above together with their cube 20-compound duals and common midspheres.


The common solids and convex hulls of these compounds are illustrated above.

See also

Cube 20-Compound, Cube-Octahedron 20-Compound, Polyhedron Conmpound

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Wenninger, M. J. Dual Models. Cambridge, England: Cambridge University Press, pp. 139-140, 1983.

Cite this as:

Weisstein, Eric W. "Octahedron 20-Compound." From MathWorld--A Wolfram Web Resource.

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