Compound of five tetrahemihexahedra

Compound of five tetrahemihexahedra
Compound of five tetrahemihexahedra
UC18-5 tetrahemihexahedron.png
Type Uniform compound
Index UC18
Polyhedra 5 tetrahemihexahedra
Faces 20 Triangles,
15 squares
Edges 60
Vertices 30
Symmetry group chiral icosahedral (I)
Subgroup restricting to one constituent chiral tetrahedral (T)

A compound of five tetrahemihexahedra is a uniform polyhedron compound and a symmetric arrangement of five tetrahemihexahedra. It is chiral with icosahedral symmetry (I).

Related polyhedra

Its convex hull is an icosidodecahedron. It shares its edges and triangular faces with the compound of five octahedra.

Compound of five octahedra.png
Compound of five octahedra
UC18-5 tetrahemihexahedron.png
Compound of five tetrahemihexahedra


  • Skilling, John (1976), "Uniform Compounds of Uniform Polyhedra", Mathematical Proceedings of the Cambridge Philosophical Society 79: 447–457, doi:10.1017/S0305004100052440, MR0397554 .