Compound of ten truncated tetrahedra

Compound of ten truncated tetrahedra
Type Uniform compound
Index UC56
Polyhedra 10 truncated tetrahedra
Faces 40 triangles, 40 hexagons
Edges 180
Vertices 120
Symmetry group icosahedral (Ih)
Subgroup restricting to one constituent chiral tetrahedral (T)

This uniform polyhedron compound is a composition of 10 truncated tetrahedra, formed by truncating each of the tetrahedra in the compound of 10 tetrahedra. It also results from composing the two enantiomers of the compound of 5 truncated tetrahedra.

Cartesian coordinates

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Cartesian coordinates for the vertices of this compound are all the even permutations of

(±1, ±1, ±3)
(±τ−1, ±(−τ−2), ±2τ)
(±τ, ±(−2τ−1), ±τ2)
(±τ2, ±(−τ−2), ±2)
(±(2τ−1), ±1, ±(2τ − 1))

where τ = (1+5)/2 is the golden ratio (sometimes written φ).

References

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  • Skilling, John (1976), "Uniform Compounds of Uniform Polyhedra", Mathematical Proceedings of the Cambridge Philosophical Society, 79 (3): 447–457, Bibcode:1976MPCPS..79..447S, doi:10.1017/S0305004100052440, MR 0397554, S2CID 123279687.