Compound of six decagonal prisms
{{Short description|Polyhedral compound}}
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!bgcolor=#e7dcc3 colspan=2|Compound of six decagonal prisms | |
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| bgcolor=#e7dcc3|Type | Uniform compound |
| bgcolor=#e7dcc3|Index | UC40 |
| bgcolor=#e7dcc3|Polyhedra | 6 decagonal prisms |
| bgcolor=#e7dcc3|Faces | 12 decagons, 60 squares |
| bgcolor=#e7dcc3|Edges | 180 |
| bgcolor=#e7dcc3|Vertices | 120 |
| bgcolor=#e7dcc3|Symmetry group | icosahedral (Ih) |
| bgcolor=#e7dcc3|Subgroup restricting to one constituent | 5-fold antiprismatic (D5d) |
This uniform polyhedron compound is a symmetric arrangement of 6 decagonal prisms, aligned with the axes of fivefold rotational symmetry of a dodecahedron.
Cartesian coordinates
Cartesian coordinates for the vertices of this compound are all the cyclic permutations of
: (±√(τ−1/√5), ±2τ, ±√(τ/√5))
: (±(√(τ−1/√5)−τ2), ±1, ±(√(τ/√5)+τ))
: (±(√(τ−1/√5)−τ), ±τ2, ±(√(τ/√5)+1))
: (±(√(τ−1/√5)+τ), ±τ2, ±(√(τ/√5)−1))
: (±(√(τ−1/√5)+τ2), ±1, ±(√(τ/√5)−τ))
where τ = (1+√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|issue=3|pages=447–457|year=1976|doi=10.1017/S0305004100052440|bibcode=1976MPCPS..79..447S |mr=0397554|s2cid=123279687 }}.
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