■サマーヴィルの等面四面体(その257)

 G6のP5から,P1P2,P2P3,P3P4方向に伸長させた点をP0とする.

[1]P5+P1P2方向(5/√10,√14/2,0,0)

P0(11/√10,√14/2,42/√560,21/√84)

P1(0,0,0,0)

P2(5/√10,(√14)/2,0,0)

P3(10/√10,0,0,0)

P4(8/√10,0,56/√560,0)

P5(6/√10,0,42/√560,21/√84)

  P1P0^2=121/10+14/4+63/20+21/4  (NG)  P2P0^2=36/10+63/20+21/4=12

  P3P0^2=1/10+14/4+63/20+21/4=12

  P4P0^2=9/10+14/4+7/20+21/4=10

  P5P0^2=25/10+14/4=6

[2]P5−P1P2方向(−5/√10,−√14/2,0,0)

P0(1/√10,−√14/2,42/√560,21/√84)

P1(0,0,0,0)

P2(5/√10,(√14)/2,0,0)

P3(10/√10,0,0,0)

P4(8/√10,0,56/√560,0)

P5(6/√10,0,42/√560,21/√84)

  P1P0^2=1/10+14/4+63/20+21/42=12

  P2P0^2=16/10+14+63/20+21/4  (NG)

[3]P5+P2P3方向(5/√10,−√14/2,0,0)

P0(11/√10,−√14/2,42/√560,21/√84)

P1(0,0,0,0)

P2(5/√10,(√14)/2,0,0)

P3(10/√10,0,0,0)

P4(8/√10,0,56/√560,0)

P5(6/√10,0,42/√560,21/√84)

  P1P0^2=121/10+14/4+63/20+21/4  (NG)

[4]P5−P2P3方向(5/√10,−√14/2,0,0)

P0(11/√10,−√14/2,42/√560,21/√84)

P1(0,0,0,0)

P2(5/√10,(√14)/2,0,0)

P3(10/√10,0,0,0)

P4(8/√10,0,56/√560,0)

P5(6/√10,0,42/√560,21/√84)

  P1P0^2=121/10+・・・  (NG)

[5]P5+P3P4方向(−2/√10,0,56/√560,0)

P0(4/√10,0,98/√560,21/√84)

P1(0,0,0,0)

P2(5/√10,(√14)/2,0,0)

P3(10/√10,0,0,0)

P4(8/√10,0,56/√560,0)

P5(6/√10,0,42/√560,21/√84)

  P1P0^2=16/10+343/20+21/4  (NG)

[6]P5−P3P4方向(−2/√10,0,56/√560,0)

P0(4/√10,0,98/√560,21/√84)

P1(0,0,0,0)

P2(5/√10,(√14)/2,0,0)

P3(10/√10,0,0,0)

P4(8/√10,0,56/√560,0)

P5(6/√10,0,42/√560,21/√84)

  P1P0^2=16/10+343/20+21/4  (NG)

 またしても解が見つからない.

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