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A compound with the symmetry of the Cube which arises by joining four Cubes such that each 
axis falls along the axis of one of the other Cubes (Holden 1971, p. 35).
See also Cube, Cube 2-Compound, Cube 3-Compound, Cube 5-Compound, Polyhedron Compound
References
Holden, A. Shapes, Space, and Symmetry. New York: Dover, 1991.