■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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