Compound of six decagonal prisms

Compound of six decagonal prismsTypeUniform compoundIndexUC40Polyhedra6 decagonal prismsFaces12 decagons,60 squaresEdges180Vertices120Symmetry groupicosahedral (Ih)Subgroup restricting to one constituent5-fold antiprismatic (D5d) This uniform polyhedron compound is a symmetric arrangement of 6 decagonal prisms, aligned with the axes of fivefold rotational symmetry of a dodecahedron.

Cartesian coordinates Cartesian coordinates for the vertices of this compound are all the cyclic permutations of

(±√(τ−1/√5), ±2τ, ±√(τ/√5)) (±(√(τ−1/√5)−τ2), ±1, ±(√(τ/√5)+τ)) (±(√(τ−1/√5)−τ), ±τ2, ±(√(τ/√5)+1)) (±(√(τ−1/√5)+τ), ±τ2, ±(√(τ/√5)−1)) (±(√(τ−1/√5)+τ2), ±1, ±(√(τ/√5)−τ))

where τ = (1+√5)/2 is the golden ratio (sometimes written φ).

References .