■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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