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・ Snub heptaheptagonal tiling
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Snub icosidodecadodecahedron
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Snub icosidodecadodecahedron : ウィキペディア英語版
Snub icosidodecadodecahedron

In geometry, the snub icosidodecadodecahedron is a nonconvex uniform polyhedron, indexed as U46.
== Cartesian coordinates ==
Cartesian coordinates for the vertices of a snub icosidodecadodecahedron are all the even permutations of
: (±2α, ±2γ, ±2β),
: (±(α+β/τ+γτ), ±(-ατ+β+γ/τ), ±(α/τ+βτ-γ)),
: (±(-α/τ+βτ+γ), ±(-α+β/τ-γτ), ±(ατ+β-γ/τ)),
: (±(-α/τ+βτ-γ), ±(α-β/τ-γτ), ±(ατ+β+γ/τ)) and
: (±(α+β/τ-γτ), ±(ατ-β+γ/τ), ±(α/τ+βτ+γ)),
with an even number of plus signs, where
: α = ρ+1,
: β = τ2ρ22ρ+τ,
: γ = ρ2+τρ,
and where τ = (1+√5)/2 is the golden mean and
ρ is the real solution to ρ3=ρ+1, or approximately 1.3247180.
ρ is called the plastic constant.
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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