Compound of ten hexagonal prisms

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−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


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