Compound of four octahedra
# Compound of four octahedra

Compound of four octahedra :

| Type | Uniform compound |
| - | - |
| Index | $UC_{12}$ |
| Convex hull | Nonuniform truncated cube |
| Polyhedra | 4 octahedra |
| Faces | 8+24 triangles |
| Edges | 48 |
| Vertices | 24 |
| Symmetry group | octahedral $(O_h)$ |
| Subgroup restricting to one constituent | 3-fold antiprismatic $(D_{3d})$ |

The compound of four octahedra is a uniform polyhedron compound. It's composed of a symmetric arrangement of 4 octahedra, considered as triangular antiprisms. It can be constructed by superimposing four identical octahedra, and then rotating each by 60 degrees about a separate axis (that passes through the centres of two opposite octahedral faces).

Its dual is the compound of four cubes.

## Cartesian coordinates

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

    (±2, ±1, ±2)
