Compound of five truncated tetrahedra

Compound of five truncated tetrahedra

Type	Uniform compound
Index	UC₅₅
Polyhedra	5 truncated tetrahedra
Faces	20 triangles, 20 hexagons
Edges	90
Vertices	60
Dual
Symmetry group	chiral icosahedral (I)
Subgroup restricting to one constituent	chiral tetrahedral (T)

3D model of a 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.

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

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