Английская Википедия:Compound of five truncated cubes

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Шаблон:Short description

Compound of five truncated cubes
Файл:UC57-5 truncated cubes.png
Type Uniform compound
Index UC57
Polyhedra 5 truncated cubes
Faces 40 triangles, 30 octagons
Edges 180
Vertices 120
Symmetry group icosahedral (Ih)
Subgroup restricting to one constituent pyritohedral (Th)

This uniform polyhedron compound is a composition of 5 truncated cubes, formed by truncating each of the cubes in the compound of 5 cubes.

Cartesian coordinates

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

(±(2+Шаблон:Radic), ±Шаблон:Radic, ±(2+Шаблон:Radic))
(±τ, ±(τ−1−1Шаблон:Radic), ±(2τ−1+τШаблон:Radic))
(±1, ±(τ−2−τ−1Шаблон:Radic), ±(τ2Шаблон:Radic))
(±(1+Шаблон:Radic), ±(−τ−2Шаблон:Radic), ±(τ2+Шаблон:Radic))
(±(τ+τШаблон:Radic), ±(−τ−1), ±(2τ−1+τ−1Шаблон:Radic))

where τ = (1+Шаблон:Radic)/2 is the golden ratio (sometimes written φ).

References


Шаблон:Polyhedron-stub