Compound of ten truncated tetrahedra
# Compound of ten truncated tetrahedra

Compound of ten truncated tetrahedra :

| Type | Uniform compound |
| - | - |
| Index | $UC_{56}$ |
| 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, $±(−2τ^{−1}),$ $±τ^2)$
    $(±τ^2,$ $±(−τ^{−2}),$ ±2)
    (±(2τ−1), ±1, ±(2τ − 1))

where τ = (1+√5)/2 is the golden ratio (sometimes written φ).

