- Inverted snub dodecadodecahedron
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Inverted snub dodecadodecahedron 
Type Uniform star 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, [5,3]+, 532 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. It is given a Schläfli symbol s{5/3,5}.
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 root of 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.
See also
External links
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