Compound of twenty octahedra

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Compound of twenty octahedra
UC14-20 octahedra.png
Type Uniform compound
Index UC14
Polyhedra 20 octahedra
Faces 40+120 triangles
Edges 240
Vertices 60
Symmetry group icosahedral (Ih)
Subgroup restricting to one constituent 6-fold improper rotation (S6)

This uniform polyhedron compound is 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.

Related polyhedra[edit]

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.png
Great snub dodecicosidodecahedron
Great dirhombicosidodecahedron.png
Great dirhombicosidodecahedron
Great disnub dirhombidodecahedron.png
Great disnub dirhombidodecahedron
UC14-20 octahedra.png
Compound of twenty octahedra
UC19-20 tetrahemihexahedron.png
Compound of twenty tetrahemihexahedra

See also[edit]


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