Compound of three cubes
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| Compound of three cubes | |
|---|---|
 |
|
| 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).
This compound famously appears in the lithograph print Waterfall by M.C. Escher.
[edit] Cartesian coordinates
Cartesian coordinates for the vertices of this compound are all the permutations of
- (±√2, 0, ±1)
[edit] References
- John Skilling, Uniform Compounds of Uniform Polyhedra, Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 79, pp. 447-457, 1976.
