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.

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

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

(11)

(12)

(13)

The hull of this compound has surface area

(14)

compared to
for each of the six constituent cubes.