■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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