■サマーヴィルの等面四面体(その533)
A=a^2,B=b^2,C=c^2,・・・
以下の付帯条件をもっと一般化できるだろうか?
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[1]3次元の場合,3A−3B+C=0
3A−3B<0
P0P1=P1P2=P2P3=a
P0P2=P1P3=b
P0P3=c
[2]4次元の場合,4A−6B+4C−D=0
4A−6B+4C>0
P0P1=P1P2=P2P3=P3P4=a
P0P2=P1P3=P2P4=b
P0P3=P1P4=c
P0P4=d
[3]5次元の場合,5A−10B+10C−5D+E=0
5A−10B+10C−5D<0
P0P1=P1P2=P2P3=P3P4=P4P5=a
P0P2=P1P3=P2P4=P3P5=b
P0P3=P1P4=P2P5=c
P0P4=P1P5=d
P0P5=e
[4]6次元の場合,6A−15B+20C−15D+6E−F=0
6A−15B+20C−15D+6E>0
P0P1=P1P2=P2P3=P3P4=P4P5=P5P6=a
P0P2=P1P3=P2P4=P3P5=P4P6=b
P0P3=P1P4=P2P5=P3P6=c
P0P4=P1P5=P2P6=d
P0P5=P1P6=e
P0P6=f
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