Compound of six pentagrammic antiprisms
|Compound of six pentagrammic antiprisms|
|Polyhedra||6 pentagrammic antiprisms|
|Faces||60 triangles, 12 pentagrams|
|Symmetry group||chiral icosahedral (I)|
|Subgroup restricting to one constituent||5-fold dihedral (D5)|
Cartesian coordinates for the vertices of this compound are all the cyclic permutations of
- (±(τ+√τ−1), ±τ−1, ±(−1+√τ))
- (±√τ−1, ±2, ±√τ)
- (±(−τ+√τ−1), ±τ−1, ±(1+√τ))
- (±(−1+√τ−1), ±(−τ), ±(τ−1+√τ))
- (±(1+√τ−1), ±(−τ), ±(−τ−1+√τ))
with an even number of minuses in the '±' choices, where τ = (1+√5)/2 is the golden ratio (sometimes written φ).
- 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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