■正多胞体の不変量(その14)
計算があわないのでいったん保留し,まとめておきたい.
ξ=2mπ/h
ξ1+ξn=ξ2+ξn-1=・・・=2π
mi+mn-i+1=h
x=cosξ/2とおくと
[3^n-1]→Un(x)=0→cosjπ/(n+1)
[3^n-2,4]→Tn(x)=0→cos(2j−1)π/2n
[3^n-3,1,1]→xTn-1(x)=0→cos(2j−1)π/2(n−1)
[3^n-4,2,1]→Un(x)−xUn-5(x)=0
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2x=2cosξ/2=yとおくと,
[3^3]→y^4−3y^2+1=0→ξ=2π/5
[3^2,1,1]→y(y^4−4y^2+2)=0→ξ=2π/8
[3^2,2,1]→(y^2−1)(y^4−4y^2+1)=0→ξ=2π/12
[3^3,2,1]→y(y^6−6y^4+9y^2−3)=0→ξ=2π/18
[3^4,2,1]→y^8−7y^6+14y^4−8y^2+1=0→ξ=2π/30
[3^5,2,1]→y(y^4−4)(y^2−1)(y^4−3y^2+1)=0→ξ=2π/0
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