Compound of six pentagrammic antiprisms

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Compound of six pentagrammic antiprisms
UC44-6 pentagrammic antiprisms.png
Type Uniform compound
Index UC44
Polyhedra 6 pentagrammic antiprisms
Faces 60 triangles, 12 pentagrams
Edges 120
Vertices 60
Symmetry group chiral icosahedral (I)
Subgroup restricting to one constituent 5-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[edit]

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).


  • Skilling, John (1976), "Uniform Compounds of Uniform Polyhedra", Mathematical Proceedings of the Cambridge Philosophical Society, 79 (3): 447–457, doi:10.1017/S0305004100052440, MR 0397554 .