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Great snub icosidodecahedron
In geometry, the great snub icosidodecahedron is a nonconvex uniform polyhedron, indexed as U57. It can be represented by a Schläfli symbol sr, and Coxeter-Dynkin diagram .
This polyhedron is the snub member of a family that includes the great icosahedron, the great stellated dodecahedron and the great icosidodecahedron.
== 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/ξ
and
: β = −ξ/τ+1/τ2−1/(ξτ),
where τ = (1+√5)/2 is the golden mean and
ξ is the negative real root of 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.
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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