Compound of four octahedra

Polyhedral compound

Compound of four octahedra

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)
3D model of a compound of four octahedra

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

[edit]

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

(±2, ±1, ±2)

## See also

[edit]

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

## References

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* Skilling, John (1976), "Uniform Compounds of Uniform Polyhedra", Mathematical Proceedings of the Cambridge Philosophical Society, 79 (3): 447–457, Bibcode:1976MPCPS..79..447S, doi:10.1017/S0305004100052440, MR 0397554, S2CID 123279687447-457&rft.date=1976&rft_id=info:doi/10.1017/S0305004100052440&rft_id=https://mathscinet.ams.org/mathscinet-getitem?mr=0397554#id-name=MR&rft_id=https://api.semanticscholar.org/CorpusID:123279687#id-name=S2CID&rft_id=info:bibcode/1976MPCPS..79..447S&rft.aulast=Skilling&rft.aufirst=John&rfr_id=info:sid/en.wikipedia.org:Compound+of+four+octahedra" class="Z3988">.

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