Compound of three cubes  

Type  Uniform compound 
Index  UC_{8} 
Convex hull  Nonuniform truncated octahedron 
Polyhedra  3 cubes 
Faces  6+12 squares 
Edges  36 
Vertices  24 
Symmetry group  octahedral (O_{h}) 
Subgroup restricting to one constituent  4fold prismatic (D_{4h}) 
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).
This compound famously appears in the lithograph print Waterfall by M.C. Escher.
Cartesian coordinates for the vertices of this compound are all the permutations of
