Compound of ten hexagonal prisms
Polyhedral compound
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This uniform polyhedron compound is a symmetric arrangement of 10 hexagonal prisms, aligned with the axes of three-fold rotational symmetry of an icosahedron.
| Compound of ten hexagonal prisms | |
|---|---|
 | |
| Type | Uniform compound |
| Index | UC39 |
| Polyhedra | 10 hexagonal prisms |
| Faces | 20 hexagons, 60 squares |
| Edges | 180 |
| Vertices | 120 |
| Symmetry group | icosahedral (Ih) |
| Subgroup restricting to one constituent | 3-fold antiprismatic (D3d) |
Cartesian coordinates
Cartesian coordinates for the vertices of this compound are all the cyclic permutations of
- (±√3, ±(τ−1−τ√3), ±(τ+τ−1√3))
- (±2√3, ±τ−1, ±τ)
- (±(1+√3), ±(1−τ√3), ±(1+τ−1√3))
- (±(τ−τ−1√3), ±√3, ±(τ−1+τ√3))
- (±(1−τ−1√3), ±(1−√3), ±(1+τ√3))
where τ = (1+√5)/2 is the golden ratio (sometimes written φ).
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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