// Workers AI · dad joke modeWhat did a compound of ten triangular prisms say? I'm a 10-sided story.

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.

Related polyhedra

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

• 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.