■正多胞体の不変量(その87)
x=λ+λ^-1=2cosξ=2cos(2mπ/h)に対しての固有方程式は,(その18)とはかなり異なるものになる.
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[3,3]=A3,h=4 →x=0
[3,3,3]=A4,h=5→x^2+x−1=0
[3^4]=A5,h=6 →x^2−1=0
[3^5]=A6,h=7 →x^3+x^2−2x−1=0
[3^6]=A7,h=8 →x^3−2x=0
[3^7]=A8,h=9 →x^4+x^3−3x^2−2x+1=0
[3^8]=A9,h=10 →x^4−3x^2+1=0
[3,4]=B3,h=6 →x−1=0
[3,3,4]=B4,h=8→x^2−2=0
[3^3,4]=B5,h=10→x^2−x−1=0
[3^4,4]=B6,h=12→x^3−3x=0
[3^5,4]=B7,h=14→x^3−x^2−2x+1=0
[3^6,4]=B8,h=16→x^4−4x^2+2=0
[3^7,4]=B9,h=18→x^4−x^3−3x^2+2x+1=0
[3^1,1,1]=D4,h=6 →x^2+x−2=0
[3^2,1,1]=D5,h=8 →x^2−2=0
[3^3,1,1]=D6,h=10→x^3+x^2−3x−2=0
[3^4,1,1]=D7,h=12→x^3−3x=0
[3^5,1,1]=D8,h=14→x^3+x^3−4x^2−3x+2=0
[3^6,1,1]=D9,h=16→x^4−4x^2+2=0
[3^2,2,1]=E6,h=12→x^3+x^2−3x−3=0
[3^3,2,1]=E7,h=18→x^3−3x−1=0
[3^4,2,1]=E8,h=30→x^4+x^3−4x^2−4x+1=0
[2,4,3]=F4,h=12→x^2−3=0
[3,5]=H3,h=10 →x−τ=0
[3,3,5]=H4,h=30→x^2−τ^-1x−τ^2=0
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