■サマーヴィルの等面四面体(その254)
G6P2から,P3P4,P4P5方向に伸長させた点をP0とする.
[1]P2+P3P4方向(−2/√10,0,56/√560,0)
P0(3/√10,√14/2,56/√560,0)
P1(0,0,0,0)
P2(5/√10,(√14)/2,0,0)
P3(10/√10,0,0,0)
P4(8/√10,0,56/√560,0)
P5(6/√10,0,42/√560,21/√84)
P1P0^2=9/10+14/4+56/10=10
P2P0^2=4/10+56/10=6
P3P0^2=49/10+14/4+56/10=14 (NG)
[2]P2−P3P4方向(2/√10,0,−56/√560,0)
P0(7/√10,√14/2,−56/√560)
P1(0,0,0,0)
P2(5/√10,(√14)/2,0,0)
P3(10/√10,0,0,0)
P4(8/√10,0,56/√560,0)
P5(6/√10,0,42/√560,21/√84)
P1P0^2=49/10+14/4+56/10=14 (NG)
[3]P2+P4P5方向(−2/√10,0,−14/√560,21/√84)
P0(3/√10,√14/2,−14/√560,21/√84)
P1(0,0,0,0)
P2(5/√10,(√14)/2,0,0)
P3(10/√10,0,0,0)
P4(8/√10,0,56/√560,0)
P5(6/√10,0,42/√560,21/√84)
P1P0^2=9/10+14/4+7/20+21/4=35/4+25//20=10
P2P0^2=4/10+7/20+21/4=6
P3P0^2=49/10+14/4+7/20+21/4=12
P4P0^2=25/10+14/4+35/4+21/4 (NG)
[4]P2−P4P5方向(2/√10,0,14/√560,−21/√84)
P0(7/√10,√14/2,14/√560,−21/√84)
P1(0,0,0,0)
P2(5/√10,(√14)/2,0,0)
P3(10/√10,0,0,0)
P4(8/√10,0,56/√560,0)
P5(6/√10,0,42/√560,21/√84)
P1P0^2=49/10+14/4+7/20+21/4=35/4+25/20=10
P2P0^2=4/10+7/20+21/4=6
P3P0^2=9/10+14/4+7/20+21/4=10
P4P0^2=1/10+14/4+63/20+21/4=12
P5P0^2=1/10+14/4+14/10+21 (NG)
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