Micromagnetics

Template:Uniform polyhedra db In geometry, the great retrosnub icosidodecahedron is a nonconvex uniform polyhedron, indexed as U₇₄. It is given a Schläfli symbol s{3/2,5/3}.

Cartesian coordinates

Cartesian coordinates for the vertices of a great retrosnub 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 smaller positive real root of ξ³−2ξ=−1/τ, namely

$\xi =\frac{(1+i\sqrt{3}){(\frac{1}{2\tau }+\sqrt{\frac{{\tau }^{-2}}{4}-\frac{8}{27}})}^{\frac{1}{3}}+(1-i\sqrt{3}){(\frac{1}{2\tau }-\sqrt{\frac{{\tau }^{-2}}{4}-\frac{8}{27}})}^{\frac{1}{3}}}{2}$

or approximately 0.3264046. 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
• Great snub icosidodecahedron
• Great inverted snub icosidodecahedron

External links

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• http://gratrix.net/polyhedra/uniform/summary