- Compound of six pentagrammic crossed antiprisms
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Compound of six pentagrammic crossed antiprisms 
Type Uniform compound Index UC29 Polyhedra 6 pentagrammic crossed antiprisms Faces 60 triangles, 12 pentagrams Edges 120 Vertices 60 Symmetry group icosahedral (Ih) Subgroup restricting to one constituent 5-fold antiprismatic (D5d) This uniform polyhedron compound is a symmetric arrangement of 6 pentagrammic crossed antiprisms. It can be constructed by inscribing within a great icosahedron one pentagrammic crossed antiprism in each of the six possible ways, and then rotating each by 36 degrees about its axis (that passes through the centres of the two opposite pentagrammic faces). It shares its vertices with the compound of 6 pentagonal antiprisms.
Cartesian coordinates
Cartesian coordinates for the vertices of this compound are all the cyclic permutations of
- (±(3−4τ−1), 0, ±(4+3τ−1))
- (±(2+4τ−1), ±τ−1, ±(1+2τ−1))
- (±(2−τ−1), ±1, ±(4−2τ−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: 447–457, doi:10.1017/S0305004100052440, MR0397554.
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