Compound of five truncated tetrahedra

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Compound of five truncated tetrahedra

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.

Compound of five truncated tetrahedra
TypeUniform compound
IndexUC55
Polyhedra5 truncated tetrahedra
Faces20 triangles, 20 hexagons
Edges90
Vertices60
DualCompound of five triakis tetrahedra
Symmetry groupchiral icosahedral (I)
Subgroup restricting to one constituentchiral tetrahedral (T)
3D model of a compound of five truncated tetrahedra

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 (3): 447–457, doi:10.1017/S0305004100052440, MR 0397554.


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