Compound of five stellated truncated hexahedra
# Compound of five stellated truncated hexahedra

Compound of five stellated truncated hexahedra :

| Type | Uniform compound |
| - | - |
| Index | $UC_{58}$ |
| Polyhedra | 5 stellated truncated hexahedra |
| Faces | 40 triangles, 30 octagrams |
| 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 stellated truncated hexahedra, formed by star-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))
    (±φ, $±(φ^{−1}−φ^{−1}√2),$ ±(2φ−1−φ√2))
    (±1, $±(φ^{−2}+φ^{−1}√2),$ $±(φ^2−φ√2))$
    (±(1−√2), $±(−φ^{−2}+√2),$ $±(φ^2−√2))$
    (±(φ−φ√2), $±(−φ^{−1}),$ $±(2φ−1−φ^{−1}√2))$

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

