Compound of ten hexagonal prisms explained

bgcolor=#e7dcc3 colspan=2	Compound of ten hexagonal prisms
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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)

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

(±, ±(τ⁻¹−τ), ±(τ+τ⁻¹))

(±2, ±τ⁻¹, ±τ)

(±(1+), ±(1−τ), ±(1+τ⁻¹))

(±(τ−τ⁻¹), ±, ±(τ⁻¹+τ))

(±(1−τ⁻¹), ±(1−), ±(1+τ))

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