| Compound of five truncated tetrahedra | |
|---|---|
| Type | Uniform compound |
| Index | UC55 |
| Polyhedra | 5 truncated tetrahedra |
| Faces | 20 triangles, 20 hexagons |
| Edges | 90 |
| Vertices | 60 |
| Dual | Compound of five triakis tetrahedra |
| Symmetry group | chiral icosahedral (I) |
| Subgroup restricting to one constituent | chiral tetrahedral (T) |
The compound of five truncated tetrahedra is a uniform polyhedron compound. It's composed of 5 truncated tetrahedra rotated around a common axis. It may be formed by truncating each of the tetrahedra in the compound of five tetrahedra. A far-enough truncation creates the compound of five octahedra. Its convex hull is a nonuniform snub dodecahedron.
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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).
- 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.