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Compound of twenty triangular prisms

Polyhedral compound From Wikipedia, the free encyclopedia

Compound of twenty triangular prisms
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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.

Compound of twenty triangular prisms
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TypeUniform compound
IndexUC33
Polyhedra20 triangular prisms
Faces40 triangles, 60 squares
Edges180
Vertices60
Symmetry groupicosahedral (Ih)
Subgroup restricting to one constituent3-fold dihedral (D3)

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.

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

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convex hull
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Rhombidodecadodecahedron
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Icosidodecadodecahedron
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Rhombicosahedron
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Compound of ten triangular prisms
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Compound of twenty triangular prisms

References

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


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