Compound of twelve pentagrammic prisms

Compound of twelve pentagrammic prisms
Compound of twelve pentagrammic prisms
UC37-12 pentagrammic prisms.png
Type Uniform compound
Index UC37
Polyhedra 12 pentagrammic prisms
Faces 24 pentagrams, 60 squares
Edges 180
Vertices 60
Symmetry group icosahedral (Ih)
Subgroup restricting to one constituent 5-fold dihedral (D5)

This uniform polyhedron compound is a symmetric arrangement of 12 pentagrammic prisms, aligned in pairs with the axes of fivefold rotational symmetry of a dodecahedron.

It results from composing the two enantiomorphs of the compound of six pentagrammic prisms. In doing so, the vertices of the two enantiomorphs coincide, with the result that the full compound has two pentagrammic prisms incident on each of its vertices.

Related polyhedra

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

Small rhombicosidodecahedron.png
Rhombicosidodecahedron		 Small dodecicosidodecahedron.png
Small dodecicosidodecahedron		 Small rhombidodecahedron.png
Small rhombidodecahedron
Small stellated truncated dodecahedron.png
Small stellated truncated dodecahedron		 UC36-6 pentagrammic prisms.png
Compound of six pentagrammic prisms		 UC37-12 pentagrammic prisms.png
Compound of twelve pentagrammic prisms

References

  • Skilling, John (1976), "Uniform Compounds of Uniform Polyhedra", Mathematical Proceedings of the Cambridge Philosophical Society 79 (03): 447–457, doi:10.1017/S0305004100052440, MR0397554 .


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