- Great inverted snub icosidodecahedron
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Great inverted snub icosidodecahedron 
Type Uniform star polyhedron Elements F = 92, E = 150
V = 60 (χ = 2)Faces by sides (20+60){3}+12{5/2} Wythoff symbol |5/3 2 3 Symmetry group I, [5,3]+, 532 Index references U69, C73, W113 
34.5/3
(Vertex figure)
Great inverted pentagonal hexecontahedron
(dual polyhedron)In geometry, the great inverted snub icosidodecahedron is a uniform star polyhedron, indexed as U69. It is given a Schläfli symbol s{5/3,3}.
Cartesian coordinates
Cartesian coordinates for the vertices of a great inverted snub icosidodecahedron are all the even permutations of
- (±2α, ±2, ±2β),
- (±(α−βτ−1/τ), ±(α/τ+β−τ), ±(−ατ−β/τ−1)),
- (±(ατ−β/τ+1), ±(−α−βτ+1/τ), ±(−α/τ+β+τ)),
- (±(ατ−β/τ−1), ±(α+βτ+1/τ), ±(−α/τ+β−τ)) and
- (±(α−βτ+1/τ), ±(−α/τ−β−τ), ±(−ατ−β/τ+1)),
with an even number of plus signs, where
- α = ξ−1/ξ
and
- β = −ξ/τ+1/τ2−1/(ξτ),
where τ = (1+√5)/2 is the golden mean and ξ is the greater positive real solution to ξ3−2ξ=−1/τ, or approximately 1.2224727. 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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