// Workers AI · dad joke modeWhat did a compound of six pentagonal prisms say? I'm a complex figure.

Compound of six pentagonal prisms
Type	Uniform compound
Index	UC34
Polyhedra	6 pentagonal prisms
Faces	12 pentagons, 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 six pentagonal prisms, aligned with the axes of fivefold rotational symmetry of a dodecahedron.

Related polyhedra

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

Nonconvex great rhombicosidodecahedron	Great dodecicosidodecahedron	Great rhombidodecahedron
Truncated great dodecahedron	Compound of six pentagonal prisms	Compound of twelve pentagonal 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, S2CID 123279687.