Compound of five tetrahemihexahedra

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

Compound of five tetrahemihexahedra
TypeUniform compound
IndexUC18
Polyhedra5 tetrahemihexahedra
Faces20 triangles,
15 squares
Edges60
Vertices30
Symmetry groupchiral icosahedral (I)
Subgroup restricting to one constituentchiral tetrahedral (T)
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.


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: 447–457, doi:10.1017/S0305004100052440, MR 0397554.
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