Compound of ten hexagonal prisms
{{Short description|Polyhedral compound}}
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!bgcolor=#e7dcc3 colspan=2|Compound of ten hexagonal prisms | |
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| bgcolor=#e7dcc3|Type | Uniform compound |
| bgcolor=#e7dcc3|Index | UC39 |
| bgcolor=#e7dcc3|Polyhedra | 10 hexagonal prisms |
| bgcolor=#e7dcc3|Faces | 20 hexagons, 60 squares |
| bgcolor=#e7dcc3|Edges | 180 |
| bgcolor=#e7dcc3|Vertices | 120 |
| bgcolor=#e7dcc3|Symmetry group | icosahedral (Ih) |
| bgcolor=#e7dcc3|Subgroup restricting to one constituent | 3-fold antiprismatic (D3d) |
This uniform polyhedron compound is a symmetric arrangement of 10 hexagonal prisms, aligned with the axes of three-fold rotational symmetry of an icosahedron.
Cartesian coordinates
Cartesian coordinates for the vertices of this compound are all the cyclic permutations of
: (±{{radic|3}}, ±(τ−1−τ{{radic|3}}), ±(τ+τ−1{{radic|3}}))
: (±2{{radic|3}}, ±τ−1, ±τ)
: (±(1+{{radic|3}}), ±(1−τ{{radic|3}}), ±(1+τ−1{{radic|3}}))
: (±(τ−τ−1{{radic|3}}), ±{{radic|3}}, ±(τ−1+τ{{radic|3}}))
: (±(1−τ−1{{radic|3}}), ±(1−{{radic|3}}), ±(1+τ{{radic|3}}))
where τ = (1+{{radic|5}})/2 is the golden ratio (sometimes written φ).
References
- {{citation|first=John|last=Skilling|title=Uniform Compounds of Uniform Polyhedra|journal=Mathematical Proceedings of the Cambridge Philosophical Society|volume=79|pages=447–457|year=1976|doi=10.1017/S0305004100052440|mr=0397554|issue=3}}.
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