- Compound of ten hexagonal prisms
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Compound of ten hexagonal prisms 
Type Uniform compound Index UC39 Polyhedra 10 hexagonal prisms Faces 20 hexagons, 60 squares Edges 180 Vertices 120 Symmetry group icosahedral (Ih) Subgroup restricting to one constituent 3-fold antiprismatic (D3d) This uniform polyhedron compound is a symmetric arrangement of 10 hexagonal prisms, aligned with the axes of three-fold rotational symmetry of an icosahedron.
Cartesian coordinates
Cartesian coordinates for the vertices of this compound are all the cyclic permutations of
- (±√3, ±(τ−1−τ√3), ±(τ+τ−1√3))
- (±2√3, ±τ−1, ±τ)
- (±(1+√3), ±(1−τ√3), ±(1+τ−1√3))
- (±(τ−τ−1√3), ±√3, ±(τ−1+τ√3))
- (±(1−τ−1√3), ±(1−√3), ±(1+τ√3))
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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