| 词条 | Snub dodecadodecahedron |
| 释义 |
In geometry, the snub dodecadodecahedron is a nonconvex uniform polyhedron, indexed as U40. It is given a Schläfli symbol sr{5/2,5}, as a snub great dodecahedron. Cartesian coordinatesCartesian coordinates for the vertices of a snub dodecadodecahedron are all the even permutations of (±2α, ±2, ±2β), (±(α+β/τ+τ), ±(-ατ+β+1/τ), ±(α/τ+βτ-1)), (±(-α/τ+βτ+1), ±(-α+β/τ-τ), ±(ατ+β-1/τ)), (±(-α/τ+βτ-1), ±(α-β/τ-τ), ±(ατ+β+1/τ)) and (±(α+β/τ-τ), ±(ατ-β+1/τ), ±(α/τ+βτ+1)), with an even number of plus signs, where β = (α2/τ+τ)/(ατ−1/τ), where τ = (1+{{radic|5}})/2 is the golden mean and α is the positive real root of τα4−α3+2α2−α−1/τ, or approximately 0.7964421. Taking the odd permutations of the above coordinates with an odd number of plus signs gives another form, the enantiomorph of the other one. {{-}}Related polyhedraMedial pentagonal hexecontahedron{{Uniform polyhedra db|Uniform dual polyhedron stat table|Siddid}}The medial pentagonal hexecontahedron is a nonconvex isohedral polyhedron. It is the dual of the snub dodecadodecahedron. It has 60 intersecting irregular pentagonal faces. See also
References
External links
1 : Uniform polyhedra |
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