Compound of twenty triangular prisms

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Compound of twenty triangular prisms
UC33-20 triangular prisms.png
Type Uniform compound
Index UC33
Polyhedra 20 triangular prisms
Faces 40 triangles, 60 squares
Edges 180
Vertices 60
Symmetry group icosahedral (Ih)
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[edit]

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

Rhombidodecadodecahedron convex hull.png
convex hull
UC32-10 triangular prisms.png
Compound of ten triangular prisms
UC33-20 triangular prisms.png
Compound of twenty triangular prisms


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