■正多胞体のポアンカレ多項式(その26)

[2,4,3]=F4,h=12→x^2−3=0

[3,3,5]=H4,h=30→x^2−τ^-1x−τ^2=0

[3^2,2,1]=E6,h=12→x^3+x^2−3x−3=0

[3^4,2,1]=E8,h=30→x^4+x^3−4x^2−4x+1=0

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x^3+x^2−3x−3=(x^2−3)(x+1)

x^4+x^3−4x^2−4x+1=(x^2−τ^-1x−τ^2)(x^2+τx−τ^-2)

はE6←→F4,E8←→H4の投影可能性を示している.

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