■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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