Compound of five truncated tetrahedra
Polyhedral compound
Compound of five truncated tetrahedra | |
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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) |
![](http://upload.wikimedia.org/wikipedia/commons/thumb/9/98/Compound_of_five_truncated_tetrahedra.stl/220px-Compound_of_five_truncated_tetrahedra.stl.png)
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.
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).
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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