Snub dodecadodecahedron
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| Snub dodecadodecahedron | |
|---|---|
 |
|
| Type | Uniform polyhedron |
| Elements | F = 84, E = 150 V = 60 (χ = -6) |
| Faces by sides | 60{3}+12{5}+12{5/2} |
| Wythoff symbol | |2 5/2 5 |
| Symmetry group | I |
| Index references | U40, C49, W111 |
 3.3.5/2.3.5 (Vertex figure) |
 Medial pentagonal hexecontahedron (dual polyhedron) |
In geometry, the snub dodecadodecahedron is a nonconvex uniform polyhedron, indexed as U40.
This polyhedron can be considered a snub great dodecahedron.
[edit] Cartesian coordinates
Cartesian 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+√5)/2 is the golden mean and α is the positive real solution to 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.
