Compound of twenty octahedra

The compound of twenty octahedra is a uniform polyhedron compound. It's composed of a symmetric arrangement of 20 octahedra (considered as triangular antiprisms). It is a special case of the compound of 20 octahedra with rotational freedom, in which pairs of octahedral vertices coincide.

Compound of twenty octahedra
TypeUniform compound
IndexUC14
Polyhedra20 octahedra
Faces40+120 triangles
Edges240
Vertices60
Symmetry groupicosahedral (Ih)
Subgroup restricting to one constituent6-fold improper rotation (S6)
3D model of a compound of twenty octahedra

This compound shares its edge arrangement with the great dirhombicosidodecahedron, the great disnub dirhombidodecahedron, and the compound of twenty tetrahemihexahedra.

It may be constructed as the exclusive or of the two enantiomorphs of the great snub dodecicosidodecahedron.


Convex hull

Great snub dodecicosidodecahedron

Great dirhombicosidodecahedron

Great disnub dirhombidodecahedron

Compound of twenty octahedra

Compound of twenty tetrahemihexahedra

See also

References

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


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