Compound of five tetrahemihexahedra

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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[edit]

Five tetrahemihexahedra in an icosidodecahedron

Its convex hull is an icosidodecahedron. Hence it is a faceting of an icosidodecahedron, shown at left. 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, MR 0397554 .