Top Qs
Timeline
Chat
Perspective
Compound of ten octahedra
Polyhedral compound From Wikipedia, the free encyclopedia
Remove ads
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.

Remove ads
Cartesian coordinates
Cartesian coordinates for the vertices of this compound are all the cyclic permutations of
- (0, ±(φ−1√2 + 2sφ), ±(φ√2 − 2sφ−1))
- (±(√2 − sτφ2), ±(√2 + s(2τφ − 1)), ±(√2 + sφ−2))
- (±(φ−1√2 − sφ), ±(φ√2 + sφ−1), ±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.
Wikiwand - on
Seamless Wikipedia browsing. On steroids.
Remove ads