Compound of six decagonal prisms
This uniform polyhedron compound is a symmetric arrangement of 6 decagonal prisms, aligned with the axes of fivefold rotational symmetry of a dodecahedron.
| Compound of six decagonal prisms | |
|---|---|
 | |
| Type | Uniform compound |
| Index | UC40 |
| Polyhedra | 6 decagonal prisms |
| Faces | 12 decagons, 60 squares |
| Edges | 180 |
| Vertices | 120 |
| Symmetry group | icosahedral (Ih) |
| Subgroup restricting to one constituent | 5-fold antiprismatic (D5d) |
Cartesian coordinates
Cartesian coordinates for the vertices of this compound are all the cyclic permutations of
- (±√(τ−1/√5), ±2τ, ±√(τ/√5))
- (±(√(τ−1/√5)−τ2), ±1, ±(√(τ/√5)+τ))
- (±(√(τ−1/√5)−τ), ±τ2, ±(√(τ/√5)+1))
- (±(√(τ−1/√5)+τ), ±τ2, ±(√(τ/√5)−1))
- (±(√(τ−1/√5)+τ2), ±1, ±(√(τ/√5)−τ))
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, Bibcode:1976MPCPS..79..447S, doi:10.1017/S0305004100052440, MR 0397554, S2CID 123279687.
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