Compound of six pentagrammic prisms

This uniform polyhedron compound is a chiral symmetric arrangement of 6 pentagrammic prisms, aligned with the axes of fivefold rotational symmetry of a dodecahedron.

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)

Related polyhedra

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

• 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.