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| Compound of six decagrammic prisms | |
|---|---|
| |
| Type | Uniform compound |
| Index | UC41 |
| Polyhedra | 6 decagrammic prisms |
| Faces | 12 decagrams, 60 squares |
| Edges | 180 |
| Vertices | 120 |
| Symmetry group | icosahedral (Ih) |
| Subgroup restricting to one constituent | 5-fold antiprismatic (D5d) |
This uniform polyhedron compound is a symmetric arrangement of 6 decagrammic prisms, aligned with the axes of fivefold rotational symmetry of a dodecahedron.
Cartesian coordinates
Cartesian coordinates for the vertices of this compound are all the cyclic permutations of
- (±√(τ/√5), ±2τ, ±√(τ/√5))
- (±(√(τ/√5)+τ), ±1, ±(√(τ/√5)−τ))
- (±(√(τ/√5)−τ), ±τ, ±(√(τ/√5)+1))
- (±(√(τ/√5)+τ), ±τ, ±(√(τ/√5)−1))
- (±(√(τ/√5)−τ), ±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.
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