■正四面体の断面(その19)
[1]3次元
b3=−b2・a2/a3
b2=−a1/(3a2)
b3=a1/(3a3)
[2]5次元
b5=−b4・a4/a5
b4=−b3・3a3/5a4
b5=b3・3a3/5a4・a4/a5=b3・3a3/5a5
b3=−b2・a2/a3
b4=b2・a2/a3・3a3/5a4=b2・3a2/5a4
b5=b3・3a3/5a5=−b2・3a2/5a5
b2=−a1/3a2
b3=a1/3a3
b4=−a1/5a4
b5=a1/5a5
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[3]4次元
b4=−b3・a3/a4
b3=−b2・a2/(2a3)
b4=b2・a2/(2a3)・a3/a4=b2・a2/(2a4)
b2=−a1/a2
b3=a1/(2a3)
b4=−a1/(2a4)
[4]6次元
b6=−b5・a5/a6
b5=−b4・(2a4)/(3a5)
b6=−b5・a5/a6=b4・(2a4)/3a6
b4=−b3・a3/a4
b5=b3・2a3/3a5
b6=−b3・(2a3)/3a6
b3=−b2・a2/2a3
b4=b2・a2/2a4
b5=−b2・a2/3a5
b6=b2・a2/3a6
b2=−a1/a2
b3=a1/2a3
b4=−a1/2a4
b5=a1/3a5
b6=−a1/3a6
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[まとめ]
[1]奇数次元では(−3,3)→(−3,3,−5,5)
[2]偶数次元では(−1,2,−2)→(−1,2,−2,3,−3)
と係数は2項単位で変化する.
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