| Compound of five stellated truncated hexahedra | |
|---|---|
| |
| Type | Uniform compound |
| Index | UC58 |
| Polyhedra | 5 stellated truncated hexahedra |
| Faces | 40 triangles, 30 octagrams |
| Edges | 180 |
| Vertices | 120 |
| Symmetry group | icosahedral (Ih) |
| Subgroup restricting to one constituent | pyritohedral (Th) |
This uniform polyhedron compound is a composition of 5 stellated truncated hexahedra, formed by star-truncating each of the cubes in the compound of 5 cubes.
Cartesian coordinates
Cartesian coordinates for the vertices of this compound are all the cyclic permutations of
- (±(2−√2), ±√2, ±(2−√2))
- (±φ, ±(φ−φ√2), ±(2φ−1−φ√2))
- (±1, ±(φ+φ√2), ±(φ−φ√2))
- (±(1−√2), ±(−φ+√2), ±(φ−√2))
- (±(φ−φ√2), ±(−φ), ±(2φ−1−φ√2))
where φ = (1+√5)/2 is the golden ratio.
References
- Skilling, John (1976), "Uniform Compounds of Uniform Polyhedra", Mathematical Proceedings of the Cambridge Philosophical Society, 79 (3): 447–457, doi:10.1017/S0305004100052440, MR 0397554.
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