■サマーヴィルの等面四面体(その255)

 G6のP3から,P1P2,P4P5方向に伸長させた点をP0とする.

[1]P3+P1P2方向(5/√10,√14/2,0,0)

P0(15/√10,√14/2,0,0)

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=225/10+14/4  (NG)

[2]P3−P1P2方向(−5/√10,−√14/2,0,0)

P0(5/√10,−√14/2,0,0)

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=25/10+14/4=6

  P2P0^2=14  (NG)

[3]P3+P4P5方向(−2/√10,0,−14/√560,21/√84)

P0(8/√10,0,−14/√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=64/10+7/20+21/4=12

  P2P0^2=9/10+14/4+7/20+21/4=10

  P3P0^2=4/10+7/20+21/4=6 

  P4P0^2=7/8+21/4  (NG)

  P5P0^2=4/10+56/10=6

[4]P3−P4P5方向(2/√10,0,14/√560,−21/√84)

P0(12/√10,0,14/√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=144/10+7/20+21/4  (NG)

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