Compound of four octahedra

Short description: Polyhedral compound

Compound of four octahedra

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Type | Uniform compound
Index | UC12
Convex hull | Nonuniform truncated cube
Polyhedra | 4 octahedra
Faces | 8+24 triangles
Edges | 48
Vertices | 24
Symmetry group | octahedral (Oh)
Subgroup restricting to one constituent | 3-fold antiprismatic (D3d)

File:Compound of four octahedra.stl 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)

## See also

* Compound of three octahedra
* Compound of five octahedra
* Compound of ten octahedra
* Compound of twenty octahedra
* Compound of four cubes

## References

* Skilling, John (1976), "Uniform Compounds of Uniform Polyhedra", Mathematical Proceedings of the Cambridge Philosophical Society 79 (3): 447–457, doi:10.1017/S0305004100052440, Bibcode: 1976MPCPS..79..447S .

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