■基本単体の二面角(その87)

 「SPLAG」第21章より,E8~を計算する.

  v1(0,0,0,0,0,0,0,1)

  v2(−1/8,1/8,1/8,1/8,1/8,1/8,1/8,7/8)

  v3(0,0,1/6,1/6,1/6,1/6,1/6,5/6)

  v4(0,0,0,1/5,1/5,1/5,1/5,4/5)

  v5(0,0,0,0,1/4,1/4,1/4,3/4)

  v6(0,0,0,0,0,1/3,1/3,2/3)

  v7(0,0,0,0,0,0,1/2,1/2)

  v8(0,0,0,0,0,0,0,0)

  v9(1/6,1/6,1/6,1/6,1/6,1/6,1/6,5/6)

  v1v2^2=1/8

  v2v3^2=2(1/8)^2+6(1/24)^2=1/32+6/576+1/144=(18+6)/576=1/24

  v3v4^2=(1/6)^2+5(1/30)^2=1/36+1/180=1/30

  v4v5^2=(1/5)^2+4(1/20)^2=1/25+1/100=1/20

  v5v6^2=(1/4)^2+3(1/12)^2=1/16+1/48=1/12

  v6v7^2=(1/3)^2+2(1/6)^2=1/9+1/18=1/6

  v7v8^2=1/2

  v3v9^2=2(1/6)^2=1/18

  (その79)と一致した.

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