Compound of ten octahedra

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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.

More information Compounds of ten octahedra ...
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)
Close
3D model of the compound of ten octahedra UC15
3D model of the compound of ten octahedra UC16

Cartesian coordinates

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

(0, ±(φ12 + 2sφ), ±(φ2 2sφ1))
(±(2 sτφ2), ±(2 + s(2τφ 1)), ±(2 + sφ2))
(±(φ12 sφ), ±(φ2 + sφ1), ±3s)

where φ = (1 + 5)/2 is the golden ratio and s is either +1 or 1. Setting s = 1 gives UC15, while s = +1 gives UC16.

See also

References

  • Skilling, John (1976), "Uniform Compounds of Uniform Polyhedra", Mathematical Proceedings of the Cambridge Philosophical Society, 79 (3): 447–457, doi:10.1017/S0305004100052440, MR 0397554.


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