Английская Википедия:Compound of ten octahedra

Материал из Онлайн справочника
Перейти к навигацииПерейти к поиску

Шаблон:Short description

Compounds of ten octahedra
Файл:UC15-10 octahedra.pngФайл:UC16-10 octahedra.png
Type Uniform compound
Index UC15 and UC16
Polyhedra 10 octahedra
Faces 20+60 triangles
Edges 120
Vertices 60
Symmetry group icosahedral (Ih)
Subgroup restricting to one constituent 3-fold antiprismatic (D3d)
Файл:First compound of ten octahedra.stl
3D model of the compound of ten octahedra UC15

Шаблон:Stack 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.

Cartesian coordinates

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

(0, ±(τ−1Шаблон:Radic + 2sτ), ±(τШаблон:Radic − 2sτ−1))
(±(Шаблон:Radicsτ2), ±(Шаблон:Radic + s(2τ − 1)), ±(Шаблон:Radic + sτ−2))
(±(τ−1Шаблон:Radicsτ), ±(τШаблон:Radic + sτ−1), ±3s)

where τ = (1 + Шаблон:Radic)/2 is the golden ratio (sometimes written φ) and s is either +1 or −1. Setting s = −1 gives UC15, while s = +1 gives UC16.

See also

References


Шаблон:Polyhedron-stub