Compound of three cubes

Compound of three cubes
TypeUniform compound
IndexUC8
Convex hullNonuniform truncated octahedron
Polyhedra3 cubes
Faces6+12 squares
Edges36
Vertices24
Symmetry groupoctahedral (Oh)
Subgroup restricting to one constituent4-fold prismatic (D4h)

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

Cartesian coordinates for the vertices of this compound are all the permutations of

2, 0, ±1)

References


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