Compound of three cubes

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Compound of three cubes
UC08-3 cubes.png
Type Uniform compound
Index UC8
Convex hull Nonuniform truncated octahedron
Polyhedra 3 cubes
Faces 6+12 squares
Edges 36
Vertices 24
Symmetry group octahedral (Oh)
Subgroup restricting to one constituent 4-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 famously 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[edit]

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

(±√2, 0, ±1)

References[edit]

  • Skilling, John (1976), Uniform Compounds of Uniform Polyhedra, Mathematical Proceedings of the Cambridge Philosophical Society 79: 447–457, doi:10.1017/S0305004100052440, MR 0397554 .