■サマーヴィルの等面四面体(その256)

 G6のP4から,P1P2,P2P3方向に伸長させた点をP0とする.

[1]P4+P1P2方向(5/√10,√14/2,0,0)

P0(13/√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=169/10+14/4+56/10  (NG)

[2]P4−P1P2方向(−5/√10,−√14/2,0,0)

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+14+56/10  (NG)

[3]P4+P2P3方向(5/√10,−√14/2,0,0)

P0(13/√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=169/10+14/4  (NG)

[4]P4−P2P3方向(−5/√10,√14/2,0,0)

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)

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