Compound of five truncated tetrahedra
|Compound of five truncated tetrahedra|
|Polyhedra||5 truncated tetrahedra|
|Faces||20 triangles, 20 hexagons|
|Dual||Compound of five triakis tetrahedra|
|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. A far-enough truncation creates the Compound of five octahedra. Its convex hull is a nonuniform Snub dodecahedron.
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: 447–457, doi:10.1017/S0305004100052440, MR 0397554.
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