This uniform polyhedron compound is a symmetric arrangement of 6 cubes, considered as square prisms. It can be constructed by superimposing six identical cubes, and then rotating them in pairs about the three axes that pass through the centres of two opposite cubic faces. Each cube is rotated by an equal (and opposite, within a pair) angle ''θ''. When ''θ'' = 0, all six cubes coincide. When ''θ'' is 45 degrees, the cubes coincide in pairs yielding (two superimposed copies of) the

compound of three cubes In geometry, the compound of three cubes is a uniform polyhedron compound formed from three cubes arranged with octahedral symmetry. It has been depicted in works by Max Brückner and M.C. Escher. History This compound appears in Max Brückner's ...

Cartesian coordinates

Cartesian coordinates A Cartesian coordinate system (, ) in a plane is a coordinate system that specifies each point uniquely by a pair of numerical coordinates, which are the signed distances to the point from two fixed perpendicular oriented lines, measured in t ...

for the vertices of this compound are all the permutations of :

(\pm(\cos(\theta)+\sin(\theta)), \pm(\cos(\theta)-\sin(\theta)), \pm1).

Gallery

File:Cube.stl, ''θ'' = 0° File:Compound of six cubes with rotational freedom (5°).stl, ''θ'' = 5° File:Compound of six cubes with rotational freedom (10°).stl, ''θ'' = 10° File:Compound of six cubes with rotational freedom (15°).stl, ''θ'' = 15° File:Compound of six cubes with rotational freedom (20°).stl, ''θ'' = 20° File:Compound of six cubes with rotational freedom (25°).stl, ''θ'' = 25° File:Compound of six cubes with rotational freedom (30°).stl, ''θ'' = 30° File:Compound of six cubes with rotational freedom (35°).stl, ''θ'' = 35° File:Compound of six cubes with rotational freedom (40°).stl, ''θ'' = 40° File:Compound of three cubes.stl, ''θ'' = 45°

References

*. Polyhedral compounds {{polyhedron-stub