Compound of ten octahedra

The compounds of ten octahedra UC15 and UC16 are two uniform polyhedron compounds. They are composed of a symmetric arrangement of 10 octahedra, considered as triangular antiprisms, aligned with the axes of three-fold rotational symmetry of an icosahedron. The two compounds differ in the orientation of their octahedra: each compound may be transformed into the other by rotating each octahedron by 60 degrees.

Compounds of ten octahedra
TypeUniform compound
IndexUC15 and UC16
Polyhedra10 octahedra
Faces20+60 triangles
Edges120
Vertices60
Symmetry groupicosahedral (Ih)
Subgroup restricting to one constituent3-fold antiprismatic (D3d)
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