Compound of five truncated tetrahedra
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| Compound of five truncated tetrahedra | |
|---|---|
 |
|
| Type | Uniform compound |
| Index | UC55 |
| Polyhedra | 5 truncated tetrahedra |
| Faces | 20 triangles, 20 hexagons |
| Edges | 90 |
| Vertices | 60 |
| Symmetry group | chiral icosahedral (I) |
| Subgroup restricting to one constituent | chiral tetrahedral (T) |
This uniform polyhedron compound is a composition of 5 truncated tetrahedra, formed by truncating each of the tetrahedra in the compound of 5 tetrahedra.
[edit] Cartesian coordinates
Cartesian coordinates for the vertices of this compound are all the cyclic permutations of
- (±1, ±1, ±3)
- (±τ−1, ±(−τ−2), ±2τ)
- (±τ, ±(−2τ−1), ±τ2)
- (±τ2, ±(−τ−2), ±2)
- (±(2τ−1), ±1, ±(2τ−1))
with an even number of minuses in the choices for '±', where τ = (1+√5)/2 is the golden ratio (sometimes written φ).
[edit] References
- John Skilling, Uniform Compounds of Uniform Polyhedra, Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 79, pp. 447-457, 1976.
