■サマーヴィルの等面四面体(その184)
P1P2=P2P3=P3P4=P4P5=√6
P1P3=P2P4=P3P5=√10
P1P4=P2P5=√12
P1P5=√12
最短辺の
P1P2=P2P3=P3P4=P4P5=√6
だけを検討したが,伸長する方向はそれ以外にあるのだろうか?
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P1から,P2P4,P3P5,P2P5方向に伸長させた点をP0とする.
[1]P1+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)
P1P0^2=36/12+14/4+14/4=10
P2P0^2=9/12+7/4+14 (NG)
[2]P1−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)
P1P0^2=36/12+14/4+14/4=10
P2P0^2=81/12+7/4+14/4=12
P3P0^2=144/12+7+14/4+14/4 (NG)
[3]P1+P3P5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)
P1P0^2=36/12+7=10
P2P0^2=9/12+7/4+14/4=6
P3P0^2=28 (NG)
[4]P1−P3P5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)
P1P0^2=36/12+7=10
P2P0^2=81/12+7/4+14/4=12
P3P0^2=144/12=12
P3P0^2=225/12+7/4+14/4 (NG)
[5]P1+P2P5方向(9/2√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+7/2+14/2=12
P2P0^2=36/12+7+14 (NG)
[6]P1−P2P5方向(−9/2√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+7/2+14/2=12
P2P0^2=144/12=12
P3P0^2=225/12+7/4+14/4 (NG)
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