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 (that passes through the centres of two opposite faces). It is also a stellation of the rhombicuboctahedron.

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

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