Compound of ten hexagonal prisms

This uniform polyhedron compound is a symmetric arrangement of 10 hexagonal prisms, aligned with the axes of three-fold rotational symmetry of an icosahedron.

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 (I_h)
Subgroup restricting to one constituent	3-fold antiprismatic (D_3d)

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).

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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