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Compound of ten octahedra

Polyhedral compound From Wikipedia, the free encyclopedia

Compound of ten octahedra
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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 ...
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3D model of the compound of ten octahedra UC15
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3D model of the compound of ten octahedra UC16
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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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