Cartesian Coordinates
Cartesian coordinates for the vertices of a great 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 negative real root of ξ3−2ξ=−1/τ, or approximately −1.5488772. Taking the odd permutations of the above coordinates with an odd number of plus signs gives another form, the enantiomorph of the other one.
Read more about this topic: Great Snub Icosidodecahedron