■サマーヴィルの等面四面体(その186)

  P1P2=P2P3=P3P4=P4P5=√6

  P1P3=P2P4=P3P5=√10

  P1P4=P2P5=√12

  P1P5=√12

 P3から,P2P4,P1P4,P2P5,P1P5方向に伸長させた点をP0とする.

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[1]P3+P2P4方向(6/2√3,0,−√14/2,√14/2)

P0(12/2√3,√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=144/12+7+14/4+14/4  (NG)

[2]P3−P2P4方向(−6/2√3,0,√14/2,−√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)

  P5P0^2=144/12+7+14/4+*14/4  (NG)

[3]P3+P1P4方向(9/2√3,(√7)/2,0,(√14)/2)

P0(15/2√3,−√7/2,0,−√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=225/12+7+14/4+14/4  (NG)

[4]P3+P1P4方向(−9/2√3,−(√7)/2,0,−(√14)/2)

P0(−6/2√3,3√7/2,0,−√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)

  P5P0^2  (NG)

[5]P3+P2P5方向(9/2√3,−√7/2,−√14/2,0)

P0(12/2√3,0,0,0)

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)

  P3P0^2=9/12+63/4+14/4  (NG)

[6]P3−P2P5方向(−9/2√3,√7/2,√14/2,0)

P0(−6/2√3,√7,√14,0)

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+7+14  (NG)

[7]P3+P1P5方向(12/2√3,0,0,0)

P0(18/2√3,√7,0,0)

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=324/12+7  (NG)

[8]P3−P1P5方向(−12/2√3,0,0,0)

P0(−6/2√3,√7,0,0)

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)

  P5P0^2=324/12+7  (NG)

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