Английская Википедия:Compound of five truncated tetrahedra

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Шаблон:Short description

Compound of five truncated tetrahedra
Файл:UC55-5 truncated tetrahedra.png
Type Uniform compound
Index UC55
Polyhedra 5 truncated tetrahedra
Faces 20 triangles, 20 hexagons
Edges 90
Vertices 60
Dual Compound of five triakis tetrahedra
Symmetry group chiral icosahedral (I)
Subgroup restricting to one constituent chiral tetrahedral (T)
Файл:Compound of five truncated tetrahedra.stl
3D model of a compound of five truncated tetrahedra

The compound of five truncated tetrahedra is a uniform polyhedron compound. It's composed of 5 truncated tetrahedra rotated around a common axis. It may be formed by truncating each of the tetrahedra in the compound of five tetrahedra. A far-enough truncation creates the compound of five octahedra. Its convex hull is a nonuniform snub dodecahedron.

Cartesian coordinates

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

(±1, ±1, ±3)
(±τ−1, ±(−τ−2), ±2τ)
(±τ, ±(−2τ−1), ±τ2)
(±τ2, ±(−τ−2), ±2)
(±(2τ−1), ±1, ±(2τ − 1))

with an even number of minuses in the choices for '±', where τ = (1+Шаблон:Radic)/2 is the golden ratio (sometimes written φ).

References


Шаблон:Polyhedron-stub