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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

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Cartesian coordinates for the vertices of this compound are all the cyclic permutations of

3, ±(τ−1−τ3), ±(τ+τ−13))
(±23, ±τ−1, ±τ)
(±(1+3), ±(1−τ3), ±(1+τ−13))
(±(τ−τ−13), ±3, ±(τ−13))
(±(1−τ−13), ±(1−3), ±(1+τ3))

where τ = (1+5)/2 is the golden ratio (sometimes written φ).

References

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  • 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.