■サマーヴィルの等面四面体(その254)

 G6P2から,P3P4,P4P5方向に伸長させた点をP0とする.

[1]P2+P3P4方向(−2/√10,0,56/√560,0)

P0(3/√10,√14/2,56/√560,0)

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=9/10+14/4+56/10=10

  P2P0^2=4/10+56/10=6

  P3P0^2=49/10+14/4+56/10=14  (NG)

[2]P2−P3P4方向(2/√10,0,−56/√560,0)

P0(7/√10,√14/2,−56/√560)

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=49/10+14/4+56/10=14  (NG)

[3]P2+P4P5方向(−2/√10,0,−14/√560,21/√84)

P0(3/√10,√14/2,−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=9/10+14/4+7/20+21/4=35/4+25//20=10

  P2P0^2=4/10+7/20+21/4=6

  P3P0^2=49/10+14/4+7/20+21/4=12

  P4P0^2=25/10+14/4+35/4+21/4  (NG)

[4]P2−P4P5方向(2/√10,0,14/√560,−21/√84)

P0(7/√10,√14/2,14/√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=49/10+14/4+7/20+21/4=35/4+25/20=10

  P2P0^2=4/10+7/20+21/4=6

  P3P0^2=9/10+14/4+7/20+21/4=10

  P4P0^2=1/10+14/4+63/20+21/4=12

  P5P0^2=1/10+14/4+14/10+21  (NG)

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