Compound of six decagrammic prisms
Polyhedral compound
Compound of six decagrammic prisms | |
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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−1, ±√(τ−1/√5))
- (±(√(τ/√5)+τ−2), ±1, ±(√(τ−1/√5)−τ−1))
- (±(√(τ/√5)−τ−1), ±τ−2, ±(√(τ−1/√5)+1))
- (±(√(τ/√5)+τ−1), ±τ−2, ±(√(τ−1/√5)−1))
- (±(√(τ/√5)−τ−2), ±1, ±(√(τ−1/√5)+τ−1))
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 (03): 447–457, doi:10.1017/S0305004100052440, MR 0397554.
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