■単純リー環を使った面数数え上げ(その35)

 ワイソフ算術を使って,以下の多胞体のf0,f1,fn-1も求めておきたい.

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【1】正単体版

  f0=(n−1)!(n+1,n−1)=(n+1)!/2

  m=n,f1=m/2・f0=n/2・f0

{3,3}(110)→f0=12(OK)

{3,3,3}(1110)→f0=60(OK)

{3,3,3,3}(1110)→f0=360(OK)

{3,3,3,3,3}(11110)→f0=2520(OK)

  f1=n/2・f0

{3,3}(110)→f1=18(OK)

{3,3,3}(1110)→f1=120(OK)

{3,3,3,3}(11110)→f1=900(OK)

{3,3,3,3,3}(111110)→f1=7560(OK)

  fn-1=2(2^n−1)−(n+1,n−1)

{3,3}(110)→f2=8(OK)

{3,3,3}(1110)→f3=20(OK)

{3,3,3,3}(11110)→f4=47(OK)

{3,3,3,3,3}(111110)→f5=105(OK)

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【2】正軸体版

  f0=(n−1)!2^n-1(n,n−1)=2^n-1n!

  m=n,f1=m/2・f0=n/2・f0

{3,4}(110)→f0=24(OK)

{3,3,4}(1110)→f0=192(OK)

{3,3,3,4}(11110)→f0=1920(OK)

{3,3,3,3,4}(111110)→f0=23040(OK)

  f1=n/2・f0

{3,4}(110)→f1=36(OK)

{3,3,4}(1110)→f1=384(OK)

{3,3,3,4}(11110)→f1=4800(OK)

{3,3,3,3,4}(111110)→f1=69120(OK)

  fn-1=3^n−1−2^n-1(n,n−1)

{3,4}(110)→f2=14(OK)

{3,3,4}(1110)→f3=48(OK)

{3,3,3,4}(11110)→f4=162(OK)

{3,3,3,3,4}(111110)→f5=536(OK)

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