Compound of ten truncated tetrahedra explained

bgcolor=#e7dcc3 colspan=2	Compound of ten truncated tetrahedra
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Type	Uniform compound
Index	UC₅₆
Polyhedra	10 truncated tetrahedra
Faces	40 triangles, 40 hexagons
Edges	180
Vertices	120
Symmetry group	icosahedral (I_h)
Subgroup restricting to one constituent	chiral tetrahedral (T)

This uniform polyhedron compound is a composition of 10 truncated tetrahedra, formed by truncating each of the tetrahedra in the compound of 10 tetrahedra. It also results from composing the two enantiomers of the compound of 5 truncated tetrahedra.

Cartesian coordinates

Cartesian coordinates for the vertices of this compound are all the even permutations of

(±1, ±1, ±3)

(±τ⁻¹, ±(−τ⁻²), ±2τ)

(±τ, ±(−2τ⁻¹), ±τ²)

(±τ², ±(−τ⁻²), ±2)

(±(2τ−1), ±1, ±(2τ − 1))

where τ = (1+)/2 is the golden ratio (sometimes written φ).