■サマーヴィルの等面四面体(その126)
面倒くさがらず,n=6の場合も検討してみたい.
P0(2/√3,0,0,0,√(7/6),√(7/2))
P1(0,0,0,0,0,0)
P2((√3)/2,(√7)/2,(√14)/2,0,0,0)
P3(√3,√7,0,0,0,0)
P4(9/√12,(√7)/2,0,(√14)/2,0,0)
P5(√12,0,0,0,0,0)
P6(4/√3,0,0,0,√(14/3),0)
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P0(4/√12, 0 ,0, 0,7/√42,7/√14)
P1( 0, 0, 0, 0, 0, 0)
P2(3/√12,7/√28,7/√14, 0, 0, 0)
P3(6/√12,14/√28, 0, 0, 0, 0)
P4(9/√12,7/√28, 0,7/√14, 0, 0)
P5(12/√12, 0 ,0, 0, 0, 0)
P6(8/√12, 0 ,0, 0,14/√42, 0)
G(6/√12, 4/√28,1/√14,1/√14,3/√42,1/√14)
GP0^2=4/12+16/28+1/14+1/14+16/42+36/14
GP1^2=36/12+16/28+1/14+1/14+9/42+1/14
GP2^2=9/12+9/28+36/14+1/14+9/42+1/14
GP3^2= 100/28+1/14+1/14+9/42+1/14
GP4^2=9/12+9/28+1/14+36/14+9/42+1/14
GP5^2=36/12+16/28+1/14+1/14+9/42+1/14
GP6^2=4/12+16/28+1/14+1/14+121/42+1/14
はすべて等しく,R^2=28/7
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