Compound of six pentagrammic antiprisms

Compound of six pentagrammic antiprisms
TypeUniform compound
IndexUC44
Polyhedra6 pentagrammic antiprisms
Faces60 triangles, 12 pentagrams
Edges120
Vertices60
Symmetry groupchiral icosahedral (I)
Subgroup restricting to one constituent5-fold dihedral (D5)

This uniform polyhedron compound is a chiral symmetric arrangement of 6 pentagrammic antiprisms, 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+τ−1), ±τ−1, ±(−1+τ))
τ−1, ±2, ±τ)
(±(−τ+τ−1), ±τ−1, ±(1+τ))
(±(−1+τ−1), ±(−τ), ±(τ−1+τ))
(±(1+τ−1), ±(−τ), ±(−τ−1+τ))

with an even number of minuses in the '±' choices, where τ = (1+√5)/2 is the golden ratio (sometimes written φ).

References


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