Cube 20-Compound


There are a number of attractive cube 20-compounds that can be constructed by taking the duals of the octahedra in the two octahedron 20-compounds. The second of these was noted and depicted by Wenninger (1983, pp. 139-140).

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

The vertices of the first cube 20-compound lead to attractive an attractive dodecahedron 6-compound, cube 6-compound, and tetrahedron 50-compound, while the second lead to a cube 25-compound and tetrahedron 50-compound (E. Weisstein, Aug. 30, 2023).


The cube 20-compound is illustrated above together with its octahedron 20-compound dual and common midsphere.


The first and second compounds have common solids that have the connectivity of a disdyakis triacontahedron and deltoidal hexecontahedron, respectively, while their convex hulls are unnamed polyhedron.

See also

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

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Verheyen, H. F. Symmetry Orbits. Boston, MA: Birkhäuser, 2007.Wenninger, M. J. Dual Models. Cambridge, England: Cambridge University Press, pp. 139-140, 1983.

Cite this as:

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

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