A number of attractive cube 6-compounds can be constructed. 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 and the convex hull is a polyhedral realization of
the graph denoted 
by Li et al. (2023; E. Weisstein, Sep. 21, 2023). 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.
