■サマーヴィルの等面四面体(その188)

  P1P2=P2P3=P3P4=P4P5=√6

  P1P3=P2P4=P3P5=√10

  P1P4=P2P5=√12

  P1P5=√12

 P5から,P1P3,P2P4,P1P4方向に伸長させた点をP0とする.

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[1]P5+P1P3方向(6/2√3,√7,0,0)

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  (NG)

[2]P5−P1P3方向(−6/2√3,−√7,0,0)

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)

  P3P0^2=28  (NG)

[3]P5+P2P4方向(6/2√3,0,−√14/2,√14/2)

P0(18/2√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  (NG)

[4]P5−P2P4方向(−6/2√3,0,√14/2,−√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)

  P4P0^2  (NG)

[5]P5+P1P4方向(9/2√3,√7/2,0,√14/2)

P0(21/2√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  (NG)

[6]P5−P1P4方向(−9/2√3,−√7/2,0,−√14/2)

P0(3/2√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)

  P4P0^2  (NG)

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