Compound of five truncated tetrahedra explained

bgcolor=#e7dcc3 colspan=2	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)

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+)/2 is the golden ratio (sometimes written φ).