Compound of four octahedra

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

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, Bibcode:1976MPCPS..79..447S, doi:10.1017/S0305004100052440, MR 0397554, S2CID 123279687.