Compound of six decagrammic prisms
# Compound of six decagrammic prisms

Compound of six decagrammic prisms :

| Type | Uniform compound |
| - | - |
| Index | $UC_{41}$ |
| Polyhedra | 6 decagrammic prisms |
| Faces | 12 decagrams, 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 decagrammic 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/√5), $±2τ^{−1},$ $±√(τ^{−1}/√5))$
    $(±(√(τ/√5)+τ^{−2}),$ ±1, $±(√(τ^{−1}/√5)−τ^{−1}))$
    $(±(√(τ/√5)−τ^{−1}),$ $±τ^{−2},$ $±(√(τ^{−1}/√5)+1))$
    $(±(√(τ/√5)+τ^{−1}),$ $±τ^{−2},$ $±(√(τ^{−1}/√5)−1))$
    $(±(√(τ/√5)−τ^{−2}),$ ±1, $±(√(τ^{−1}/√5)+τ^{−1}))$

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

