Compound of ten truncated tetrahedra
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.
| 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) |
Cartesian coordinates
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
- 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.
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