Английская Википедия:Compound of five stellated truncated hexahedra

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Шаблон:Short description

Compound of five stellated truncated hexahedra
Файл:UC58-5 quasitruncated hexahedra.png
Type Uniform compound
Index UC58
Polyhedra 5 stellated truncated hexahedra
Faces 40 triangles, 30 octagrams
Edges 180
Vertices 120
Symmetry group icosahedral (Ih)
Subgroup restricting to one constituent pyritohedral (Th)

This uniform polyhedron compound is a composition of 5 stellated truncated hexahedra, formed by star-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))
(±φ, ±(φ−1−φ−1Шаблон:Radic), ±(2φ−1−φШаблон:Radic))
(±1, ±(φ−2−1Шаблон:Radic), ±(φ2−φШаблон:Radic))
(±(1−Шаблон:Radic), ±(−φ−2+Шаблон:Radic), ±(φ2Шаблон:Radic))
(±(φ−φШаблон:Radic), ±(−φ−1), ±(2φ−1−φ−1Шаблон:Radic))

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

References


Шаблон:Polyhedron-stub