Inverted snub dodecadodecahedron
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| Inverted 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 | |5/3 2 5 |
| Symmetry group | I |
| Index references | U60, C76, W114 |
 3.3.5.3.5/3 (Vertex figure) |
 Medial inverted pentagonal hexecontahedron (dual polyhedron) |
In geometry, the inverted snub dodecadodecahedron is a nonconvex uniform polyhedron, indexed as U60.
[edit] Cartesian coordinates
Cartesian coordinates for the vertices of an inverted 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 negative real solution to τα4−α3+2α2−α−1/τ, or approximately −0.3352090. Taking the odd permutations of the above coordinates with an odd number of plus signs gives another form, the enantiomorph of the other one.
[edit] See also
[edit] External links
- Eric W. Weisstein, Inverted snub dodecadodecahedron at MathWorld.
