■正多胞体の不変量(その105)

[3^1,1,1]はt1β4=F4,{3,3,4}(0100)={3,4,3}

[3^2,1,1]はt1β5,{3,3,3,4}(01000)

[3^n,1,1]はt1βn+3

と考える.

[3]はeα2(六角形){3}(11)

[3,3]はeα3=t1β3(立方八面体){3,3}(101)

[3,3,3]=[3^3]はeα4{3,3,3}(1001)

[3,3,・・・,3]=[3^n]はeαn+1

と考える.

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E7,E6,E5=D5,E4=A4,E3=A2×A1

321,221,121=hγ5,021=t1α4,(−1)21=α2×α1

hγ4=β4,t1β4={3,4,3},hδ5={3,3,4,3}

0qr=tqαq+r*1=trαq+r*1

hγ2=α1,hγ3=α3,hγ4=β4

 pq0=αp+q+1,p11=βp+3,1q1=hγq+3

 pqrの頂点図形は(p−1)qrであるから,

0qr=tqαq*r+1=trαq+r+1=trαn  (n=q+r+1)

(−1)qr=αq×αr

空間充填図形521,331,222の頂点図形は421,231,122

0[n]=αn-1h,hδnの頂点図形はeαn,t1βn

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