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).

Compound of four octahedra
TypeUniform compound
IndexUC12
Convex hullNonuniform truncated cube
Polyhedra4 octahedra
Faces8+24 triangles
Edges48
Vertices24
Symmetry groupoctahedral (Oh)
Subgroup restricting to one constituent3-fold antiprismatic (D3d)
3D model of a compound of four octahedra

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

References

  • Skilling, John (1976), "Uniform Compounds of Uniform Polyhedra", Mathematical Proceedings of the Cambridge Philosophical Society, 79 (03): 447–457, doi:10.1017/S0305004100052440, MR 0397554.


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