Compound of three cubes

This compound appears in Max Brückner's book Vielecke und Vielflache (1900),[2] and in the lithograph print Waterfall (1961) by M.C.

Its dual, the compound of three octahedra, forms the central image in an earlier Escher woodcut, Stars.

[3] In the 15th-century manuscript De quinque corporibus regularibus, Piero della Francesca includes a drawing of an octahedron circumscribed around a cube, with eight of the cube edges lying in the octahedron's eight faces.

[4] This compound 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).

[3] Cartesian coordinates for the vertices of this compound can be chosen as all the permutations of