■サマーヴィルの等面四面体(その180)

 P2から,P3P4,P4P5方向に伸長させた点をP0とする.

[1]P2+P3P4方向(3/2√3,−√7/2,0,√14/2)

P0(6/2√3,0,√14/2,√14/2)

P1(0,0,0,0)

P2(3/2√3,(√7)/2,(√14)/2,0)

P3(6/2√3,√7,0,0)

P4(9/2√3,(√7)/2,0,(√14)/2)

P5(12/2√3,0,0,0)

  P1P0^2=36/12+14/4+14/4=10

  P2P0^2=9/12+7/4+14/4=72/12=6

  P3P0^2=7+14/4+14/4=14  (NG)

[2]P2−P3P4方向(−3/2√3,√7/2,0,−√14/2)

P0(0,√7,√14/2,−√14/2)

P1(0,0,0,0)

P2(3/2√3,(√7)/2,(√14)/2,0)

P3(6/2√3,√7,0,0)

P4(9/2√3,(√7)/2,0,(√14)/2)

P5(12/2√3,0,0,0)

  P1P0^2=7+14/4+14/4=14  (NG)

[3]P2+P4P5方向(3/2√3,−√7/2,0,−√14/2)

P0(6/2√3,0,√14/2,−√14/2)

P1(0,0,0,0)

P2(3/2√3,(√7)/2,(√14)/2,0)

P3(6/2√3,√7,0,0)

P4(9/2√3,(√7)/2,0,(√14)/2)

P5(12/2√3,0,0,0)

  P1P0^2=36/12+14/4+14/4=10

  P2P0^2=7+14/4+14/4=14  (NG)

[4]P2+P4P5方向(−3/2√3,√7/2,0,√14/2)

P0(0,√7,√14/2,√14/2)

P1(0,0,0,0)

P2(3/2√3,(√7)/2,(√14)/2,0)

P3(6/2√3,√7,0,0)

P4(9/2√3,(√7)/2,0,(√14)/2)

P5(12/2√3,0,0,0)

  P1P0^2=7+14/4+14/4=14  (NG)

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