Great inverted snub icosidodecahedron

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

• List of uniform polyhedra
• Great snub icosidodecahedron
• Great retrosnub icosidodecahedron

External links

• Weisstein, Eric W., "Great inverted snub icosidodecahedron" from MathWorld.