Compound of six decagonal prisms
# Compound of six decagonal prisms

Compound of six decagonal prisms :

| Type | Uniform compound |
| - | - |
| Index | $UC_{40}$ |
| Polyhedra | 6 decagonal prisms |
| Faces | 12 decagons, 60 squares |
| Edges | 180 |
| Vertices | 120 |
| Symmetry group | icosahedral $(I_h)$ |
| Subgroup restricting to one constituent | 5-fold antiprismatic $(D_{5d})$ |

This uniform polyhedron compound is a symmetric arrangement of 6 decagonal prisms, aligned with the axes of fivefold rotational symmetry of a dodecahedron.

## Cartesian coordinates

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

    $(±√(τ^{−1}/√5),$ ±2τ, ±√(τ/√5))
    $(±(√(τ^{−1}/√5)−τ^2),$ ±1, ±(√(τ/√5)+τ))
    $(±(√(τ^{−1}/√5)−τ),$ $±τ^2,$ ±(√(τ/√5)+1))
    $(±(√(τ^{−1}/√5)+τ),$ $±τ^2,$ ±(√(τ/√5)−1))
    $(±(√(τ^{−1}/√5)+τ^2),$ ±1, ±(√(τ/√5)−τ))

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

