Compound of ten hexagonal prisms
# Compound of ten hexagonal prisms

Compound of ten hexagonal prisms :

| Type | Uniform compound |
| - | - |
| Index | $UC_{39}$ |
| Polyhedra | 10 hexagonal prisms |
| Faces | 20 hexagons, 60 squares |
| Edges | 180 |
| Vertices | 120 |
| Symmetry group | icosahedral $(I_h)$ |
| Subgroup restricting to one constituent | 3-fold antiprismatic $(D_{3d})$ |

This uniform polyhedron compound is a symmetric arrangement of 10 hexagonal prisms, aligned with the axes of three-fold rotational symmetry of an icosahedron.

## Cartesian coordinates

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

    (±√3, $±(τ^{−1}−τ√3),$ $±(τ+τ^{−1}√3))$
    (±2√3, $±τ^{−1},$ ±τ)
    (±(1+√3), ±(1−τ√3), $±(1+τ^{−1}√3))$
    $(±(τ−τ^{−1}√3),$ ±√3, $±(τ^{−1}+τ√3))$
    $(±(1−τ^{−1}√3),$ ±(1−√3), ±(1+τ√3))

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

