■サマーヴィルの等面四面体(その183)

 P5から,P1P2,P2P3,P3P4方向に伸長させた点をP0とする.

[1]P5+P1P2方向(3/2√3,√7/2,√14/2,0)

P0(15/2√3,√7/2,√14/2,0)

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=225/12+7/4+14/4=288/12=24(NG)

  P2P0^2=144/12=12

  P3P0^2=81/12+7/4+14/4=12

  P4P0^2=36/12+14/4+14/4=10

  P5P0^2=9/12+7/4+14/4=6  (OK)

[2]P5−P1P2方向(−3/2√3,−√7/2,−√14/2,0)

P0(9/2√3,−√7/2,−√14/2,0)

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=81/12+7/4+14/4=12

  P2P0^2=36/12+7+14  (NG)

[3]P5+P2P3方向(3/2√3,√7/2,−√14/2,0)

P0(15/2√3,√7/2,−√14/2,0)

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=225/12+7/4+14/4  (NG)

[4]P5−P2P3方向(−3/2√3,−√7/2,√14/2,0)

P0(12/2√3,−√7/2,√14/2,0)

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=144/12+7/4+14/4  (NG)

[5]P5+P3P4方向(3/2√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+7/4+14/4  (NG)

[6]P5−P3P4方向(−3/2√3,√7/2,0,−√14/2)

P0(9/2√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=81/12+7/4+14/4=12

  P2P0^2=36/12+14=15  (NG)

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