■サマーヴィルの等面四面体(その150)

 △6について

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)

超平面をax+by+cz+dw+ev+fu=gとする.

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[1]P1P2P3P4P5P6平面:u=0

[2]P0P2P3P4P5P6平面:

 (1,√(6/14),√(12/14),0,√(4/14),√(12/14)),g=12/√12

[3]P0P1P3P4P5P6平面:g=0,z=0

[4]P0P1P2P4P5P6平面:g=0

 (0,1,−1/√2,−1/√2,0,0),g=0

[5]P0P1P2P3P5P6平面:g=0,w=0

[6]P0P1P2P3P4P6平面:g=0

 (1,−√(6/14),0,−√(12/14),−√(16/14),0),g=0

[7]P0P1P2P3P4P5平面:g=0

 (0,0,0,0,1,−1/√3),g=0

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