Compound of five truncated cubes
# Compound of five truncated cubes

Compound of five truncated cubes :

| Type | Uniform compound |
| - | - |
| Index | $UC_{57}$ |
| Polyhedra | 5 truncated cubes |
| Faces | 40 triangles, 30 octagons |
| Edges | 180 |
| Vertices | 120 |
| Symmetry group | icosahedral $(I_h)$ |
| Subgroup restricting to one constituent | pyritohedral $(T_h)$ |

This uniform polyhedron compound is a composition of 5 truncated cubes, formed by truncating each of the cubes in the compound of 5 cubes.

## Cartesian coordinates

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

    (±(2+√2), ±√2, ±(2+√2))
    (±τ, $±(τ^{−1}+τ^{−1}√2),$ ±(2τ−1+τ√2))
    (±1, $±(τ^{−2}−τ^{−1}√2),$ $±(τ^2+τ√2))$
    (±(1+√2), $±(−τ^{−2}−√2),$ $±(τ^2+√2))$
    (±(τ+τ√2), $±(−τ^{−1}),$ $±(2τ−1+τ^{−1}√2))$

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

