Compound of ten triangular prisms

Compound of ten triangular prisms
Type Uniform compound
Index UC32
Polyhedra 10 triangular prisms
Faces 20 triangles,
30 squares
Edges 90
Vertices 60
Symmetry group chiral icosahedral (I)
Subgroup restricting to one constituent 3-fold dihedral (D3)

This uniform polyhedron compound is a chiral symmetric arrangement of 10 triangular prisms, aligned with the axes of three-fold rotational symmetry of an icosahedron.

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

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

References

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  • 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.