■基本単体の二面角(その101)

 「SPLAG」第21章より,E6~を計算する.

  v1(0,0,0,0,0,−2/3,−2/3,2/3)

  v2(−1/4,1/4,1/4,1/4,1/4,−5/12,−5/12,5/12)

  v3(0,0,1/3,1/3,1/3,−1/3,−1/3,1/3)

  v4(0,0,0,1/2,1/2,−1/3,−1/3,1/3)

  v5(0,0,0,0,1,−1/3,−1/3,1/3)

  v6(1/4,1/4,1/4,1/4,1/4,−1/4,−1/4,1/4)

  v7(0,0,0,0,0,0,0,0)

  v6v7^2=1/2

  v5v7^2=1+1/3=4/3

  v4v7^2=1/2+1/3=5/6

  v3v7^2=2/3

  v2v7^2=5/16+75/144=5/6

  v1v7^2=12/9=4/3

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  P0(0,0,0,0,0,0)

  P1(1,0,0,0,0,0)

  P2(1,1/√3,0,0,0,0)

  P3(1,1/√3,1/√3,0,0,0)

  P4(1,1/√3,1/√3,1,0,0)

  P5(1,1/√3,0,0,1/√3,0)

  P6(1,1/√3,0,0,1/√3,1)

と一致するだろうか?

  P0P1^2=1

  P0P2^2=1+1/3=4/3

  P0P3^2=1+2/3=5/3

  P0P4^2=2+2/3=8/3

  P0P5^2=1+2/3=5/3

  P0P6^2=2=2/3=8/3

スケールは2倍になっているが一致.

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  v5v6^2=4/16+9/16+3/144=120/144=5/6

  v4v6^2=5/16+3/144=48/144=1/3

  v3v6^2=2/16+6/144=24/144=1/6

  v2v6^2=1/4+3/36=1/3

  v1v6^2=5/16+75/144=5/6

  P1P2^2=1/3

  P1P3^2=2/3

  P1P4^2=1+2/3=5/3

  P1P5^2=2/3

  P1P6^2=1+2/3=5/3

スケールは2倍になっているが一致.

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