Compound of three cubes


This uniform polyhedron compound is a symmetric arrangement of 3 cubes, considered as square prisms. It can be constructed by superimposing three identical cubes, and then rotating each by 45 degrees about a separate axis.
This compound appears in the lithograph print Waterfall by M.C. Escher. Its dual, the compound of three octahedra, forms the central image in an earlier Escher woodcut, Stars.

Cartesian coordinates

for the vertices of this compound are all the permutations of

Related compounds

If the cubes are compressed into rhombic prisms, a compound of 3 rhombic prisms is constructed. The compound has pyritohedral symmetry.
Its vertices are parametrized with lengths a and b with values besides.