■サマーヴィルの等面四面体(その832)

 B=b^2について整理してみたい.

144V^2=-a^2(c^2-a^2)^2+b^4(3a^2-2b^2+c^2)

  c^2=3(b^2-a^2)

144V^2=-a^2(c^2-a^2)^2+b^6

  4c^2=36a^2-36

  4c^2=9b^2-9

  4a^2=b^2+3,(c^2-a^2)=2b^2-3

144V^2=-(b^2+3)/4・(2b^2-3)^2+b^6

4・144V^2=-(b^2+3)・(2b^2-3)^2+4b^6

4・144V^2=-(B+3)・(2B-3)^2+4B^3

4・144V^2=-(B+3)・(4B^2-12B+9)+4B^3

=-4B^3+12B^2-9B-12B^2+36B-27+4B^3

=27B-27

B=1,C=0,A=1  (NG)

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 A=a^2について整理してみたい.

144V^2=-a^2(c^2-a^2)^2+b^6

  4c^2=36a^2-36

  4c^2=9b^2-9

  4a^2=b^2+3,(c^2-a^2)=2b^2-3=8a^2-9

144V^2=-a^2・(8a^2-9)^2+(4a^2-3)^3

=-A・(8A-9)^2+(4A-3)^3

=27A-27

A=1,C=0,N=1  (NG)

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