Compound of six pentagrammic crossed antiprisms

Compound of six pentagrammic crossed antiprisms
TypeUniform compound
IndexUC29
Polyhedra6 pentagrammic crossed antiprisms
Faces60 triangles, 12 pentagrams
Edges120
Vertices60
Symmetry groupicosahedral (Ih)
Subgroup restricting to one constituent5-fold antiprismatic (D5d)

This uniform polyhedron compound is a symmetric arrangement of 6 pentagrammic crossed antiprisms. It can be constructed by inscribing within a great icosahedron one pentagrammic crossed antiprism in each of the six possible ways, and then rotating each by 36 degrees about its axis (that passes through the centres of the two opposite pentagrammic faces). It shares its vertices with the compound of 6 pentagonal antiprisms.

Cartesian coordinates

Cartesian coordinates for the vertices of this compound are all the cyclic permutations of

(±(3−4τ−1), 0, ±(4+3τ−1))
(±(2+4τ−1), ±τ−1, ±(1+2τ−1))
(±(2−τ−1), ±1, ±(4−2τ−1))

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

References


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