Great inverted snub icosidodecahedron

Great inverted snub icosidodecahedron
TypeUniform star polyhedron
ElementsF = 92, E = 150
V = 60 (χ = 2)
Faces by sides(20+60){3}+12{5/2}
Wythoff symbol|5/3 2 3
Symmetry groupI, [5,3]+, 532
Index referencesU69, C73, W113
Dual polyhedronGreat inverted pentagonal hexecontahedron
Vertex figure
34.5/3
Bowers acronymGisid

In geometry, the great inverted snub icosidodecahedron is a uniform star polyhedron, indexed as U69. It is given a Schläfli symbol sr{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),
(±(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 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.

Great inverted pentagonal hexecontahedron

Great inverted pentagonal hexecontahedron
TypeStar polyhedron
Face
ElementsF = 60, E = 150
V = 92 (χ = 2)
Symmetry groupI, [5,3]+, 532
Index referencesDU69
dual polyhedronGreat inverted snub icosidodecahedron

The great inverted pentagonal hexecontahedron is a nonconvex isohedral polyhedron. It is composed of 60 self-intersecting pentagonal faces, 150 edges and 92 vertices.

It is the dual of the uniform great inverted snub icosidodecahedron.

See also

References


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