■基本単体の二面角(その373)

 ボロビック「鏡映の数学」に対しても,二面角を計算してみたい.

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[1]A4

  ρ1=(−1/√2,1/√2,0,0,0)

  ρ2=(0,−1/√2,1/√2,0,0)

  ρ3=(0,0,−1/√2,1/√2,0)

  ρ4=(0,0,0,−1/√2,1/√2)

  ρ1・ρ2=−1/2

[2]B4

  ρ1=(1,0,0,0)

  ρ2=(−1/√2,1/√2,0,0)

  ρ3=(0,−1/√2,1/√2,0)

  ρ4=(0,0,−1/√2,1/√2)

  ρ1・ρ2=−1/√2

  ρ2・ρ3=−1/2

[3]D4

  ρ1=(1/√2,1/√2,0,0)

  ρ2=(−1/√2,1/√2,0,0)

  ρ3=(0,−1/√2,1/√2,0)

  ρ4=(0,0,−1/√2,1/√2)

  ρ1・ρ2=−1/2

  ρ2・ρ3=−1/2

[4]E8

  ρ1=(1/2√2,−1/2√2,−1/2√2,−1/2√2,−1/2√2,−1/2√2,−1/2√2,1/2√2)

  ρ2=(1/√2,1/√2,0,0,0,0,0,0)

  ρ3=(0,−1/√2,1/√2,0,0,0,0,0)

  ρ4=(0,0,−1/√2,1/√2,0,0,0,0)

  ρ1・ρ2=0

  ρ2・ρ3=−1/2

[5]F4

  ρ1=(0,1/√2,−1/√2,0)

  ρ2=(0,0,1/√2,−1/√2)

  ρ3=(0,0,0,1)

  ρ4=(1/2,−1/2,−1/2,−1/2)

  ρ1・ρ2=−1/2

  ρ2・ρ3=−1/√2

[6]G2

  ρ1=(1/√2,−1/√2,0)

  ρ2=(−2/√6,1/√6,1/√6)

  ρ1・ρ2=−√3/2

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