Compound of ten hexagonal prisms
TypeUniform compound
IndexUC39
Polyhedra10 hexagonal prisms
Faces20 hexagons, 60 squares
Edges180
Vertices120
Symmetry groupicosahedral (Ih)
Subgroup restricting to one constituent3-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−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

  • 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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