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)

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.

• 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.

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