Compound of six decagonal prisms

Compound of six decagonal prisms
TypeUniform compound
IndexUC40
Polyhedra6 decagonal prisms
Faces12 decagons,
60 squares
Edges180
Vertices120
Symmetry 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

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

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

References