Compound of six decagrammic prisms

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Compound of six decagrammic prisms
UC41-6 decagrammic prisms.png
Type Uniform compound
IndexUC41
Polyhedra6 decagrammic prisms
Faces12 decagrams, 60 squares
Edges180
Vertices120
Symmetry group icosahedral (Ih)
Subgroup restricting to one constituent5-fold antiprismatic (D5d)

This uniform polyhedron compound is a symmetric arrangement of 6 decagrammic 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/√5), ±2τ−1, ±√(τ−1/√5))
(±(√(τ/√5)+τ−2), ±1, ±(√(τ−1/√5)−τ−1))
(±(√(τ/√5)−τ−1), ±τ−2, ±(√(τ−1/√5)+1))
(±(√(τ/√5)+τ−1), ±τ−2, ±(√(τ−1/√5)−1))
(±(√(τ/√5)−τ−2), ±1, ±(√(τ−1/√5)+τ−1))

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

References