Cube 6-compounds can be constructed in a number of attractive forms. A first (left figures) is obtained by combining six cubes, each rotated by 1/6 of a turn about the line joining the centroids of opposite faces of an initial cube. A second compound, illustrated at right, is obtained by combining six cubes, each rotated by 1/8 of a turn about the line joining the centroids of opposite faces of an initial cube.
These compounds are implemented in the Wolfram Language as PolyhedronData[
"CubeSixCompound",
n
]
for 
,
2.
These cube 6-compounds are illustrated above together with their octahedron 6-compound duals and common midspheres.
For the first compound, the common solid is an unnamed polyhedron illustrated above. E. Weisstein observed on Sep. 21, 2023, that its convex
hull is a polyhedral realization of the graph denoted 
by Li et al. (2026). For the second, the common
solid is an unnamed solid illustrated above and the convex
hull is nonregular solid with the connectivity of the great
rhombicuboctahedron.
A net for constructing the first compound is illustrated above, where
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The hull of this compound has surface area
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(14)
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compared to 
for each of the six constituent cubes.
