Great retrosnub icosidodecahedron

Great retrosnub icosidodecahedron
TypeUniform star polyhedron
ElementsF = 92, E = 150
V = 60 (χ = 2)
Faces by sides(20+60){3}+12{5/2}
Wythoff symbol|3/2 5/3 2
Symmetry groupI, [5,3]+, 532
Index referencesU74, C90, W117
Dual polyhedronGreat pentagrammic hexecontahedron
Vertex figure
(34.5/2)/2
Bowers acronymGirsid

In geometry, the great retrosnub icosidodecahedron or great inverted 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),
(±(αβτ−1/τ), ±(α/τ+βτ), ±(−ατβ/τ−1)),
(±(ατβ/τ+1), ±(−αβτ+1/τ), ±(−α/τ+β+τ)),
(±(ατβ/τ−1), ±(α+βτ+1/τ), ±(−α/τ+βτ)) and
(±(αβτ+1/τ), ±(−α/τβτ), ±(−ατβ/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

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

External links


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