Compound of four octahedra

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Compound of four octahedra
UC12-4 octahedra.png
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)

This uniform polyhedron compound is 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).

Cartesian coordinates[edit]

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

(±2, ±1, ±2)

See also[edit]


  • 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 .