Compound of five tetrahemihexahedra
Polyhedral compound
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A compound of five tetrahemihexahedra is a uniform polyhedron compound and a symmetric arrangement of five tetrahemihexahedra. It could be also called a hemirhombichiricosahedron. It is chiral with icosahedral symmetry (I).
| Compound of five tetrahemihexahedra | |
|---|---|
 | |
| 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) |
Related polyhedra
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.
 Icosidodecahedron |
 Compound of five octahedra |
Compound of five tetrahemihexahedra |
See also
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.
- McCooey, Robert. "Uniform Polyhedron Compounds". Hedron Dude. Retrieved 24 June 2025.
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