Great snub icosidodecahedron

In geometry, the great snub icosidodecahedron is a nonconvex uniform polyhedron, indexed as U₅₇.

This polyhedron can be considered a snub great icosahedron.

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/ξand: β = −ξ/τ+1/τ²−1/(ξτ),where τ = (1+√5)/2 is the golden mean andξ is the negative real solution to 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.

See also

* List of uniform polyhedra

External links

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