compound of twenty triangular prisms
{{Short description|Polyhedral compound}}
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!bgcolor=#e7dcc3 colspan=2|Compound of twenty triangular prisms | |
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| bgcolor=#e7dcc3|Type | Uniform compound |
| bgcolor=#e7dcc3|Index | UC33 |
| bgcolor=#e7dcc3|Polyhedra | 20 triangular prisms |
| bgcolor=#e7dcc3|Faces | 40 triangles, 60 squares |
| bgcolor=#e7dcc3|Edges | 180 |
| bgcolor=#e7dcc3|Vertices | 60 |
| bgcolor=#e7dcc3|Symmetry group | icosahedral (Ih) |
| bgcolor=#e7dcc3|Subgroup restricting to one constituent | 3-fold dihedral (D3) |
This uniform polyhedron compound is a symmetric arrangement of 20 triangular prisms, aligned in pairs with the axes of three-fold rotational symmetry of an icosahedron.
It results from composing the two enantiomorphs of the compound of 10 triangular prisms. In doing so, the vertices of the two enantiomorphs coincide, with the result that the full compound has two triangular prisms incident on each of its vertices.
Related polyhedra
This compound shares its vertex arrangement with three uniform polyhedra as follows:
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| 100px Rhombicosahedron | 100px | 100px |
References
- {{citation|first=John|last=Skilling|title=Uniform Compounds of Uniform Polyhedra|journal=Mathematical Proceedings of the Cambridge Philosophical Society|volume=79|issue=3|pages=447–457|year=1976|doi=10.1017/S0305004100052440|mr=0397554}}.
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