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Compound of six pentagrammic prisms

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Compound of six pentagrammic prisms
Type Uniform compound
Index UC36
Polyhedra 6 pentagrammic prisms
Faces 12 pentagrams, 30 squares
Edges 90
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 prisms, aligned with the axes of fivefold rotational symmetry of a dodecahedron.

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This compound shares its vertex arrangement with four uniform polyhedra as follows:


Rhombicosidodecahedron

Small dodecicosidodecahedron

Small rhombidodecahedron

Small stellated truncated dodecahedron

Compound of six pentagrammic prisms

Compound of twelve pentagrammic prisms

References

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