Compound of ten hexagonal prisms

Compound of ten hexagonal prismsTypeUniform compoundIndexUC39Polyhedra10 hexagonal prismsFaces20 hexagons, 60 squaresEdges180Vertices120Symmetry 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

(±, ±(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).

References .