Compound of six decagrammic prisms

Compound of six decagrammic prisms
TypeUniform compound
IndexUC41
Polyhedra6 decagrammic prisms
Faces12 decagrams, 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 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, ±−1/5))
(±((τ/5)+τ−2), ±1, ±(−1/5)−τ−1))
(±((τ/5)−τ−1), ±τ−2, ±(−1/5)+1))
(±((τ/5)+τ−1), ±τ−2, ±(−1/5)−1))
(±((τ/5)−τ−2), ±1, ±(−1/5)+τ−1))

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

References


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