■サマーヴィルの等面四面体(その362)

 △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)

  P0P1=P1P2=P2P3=P3P4=P4P5=P5P6=√6

  P0P2=P1P3=P2P4=P3P5=P4P6=√10

  P0P3=P1P4=P2P5=P3P6=√12

  P0P4=P1P5=P2P6=√12

  P0P5=P1P6=√10

  P0P6=√6

[1]P1P2P3P4P5P6平面:a

[2]P0P2P3P4P5P6平面:b

[3]P0P1P3P4P5P6平面:c

[4]P0P1P2P4P5P6平面:d

[5]P0P1P2P3P5P6平面:e

[6]P0P1P2P3P4P6平面:f=0

[7]P0P1P2P3P4P5平面:g=0

  a=(0,0,0,0,0,1)

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

  c=(0,0,1,0,0,0)

  d=(0,1,−1/√2,−1/√2,0,0)

  e=(0,0,0,1,0,0)

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

  g=(0,0,0,0,1,−1/√3)

を正規化すると

  a=(0,0,0,0,0,1)

  b=(1/√48/14,1/√8,1/√4,0,1/√12,1/√4)

  c=(0,0,1,0,0,0)

  d=(0,1/√2,−1/2,−1/2,0,0)

  e=(0,0,0,1,0,0)

  f=(1/√48/14,−1/√8,0,−1/√4,−1/√3,0)

  g=(0,0,0,0,√3/2,−1/2)

a・b=1/2

a・c=0

a・d=0

a・e=0

a・f=0

a・g=−1/2

b・c=1/2

b・d=0

b・e=0

b・f=0

b・g=0

c・d=−1/2

c・e=0

c・f=0

c・g=0

d・e=−1/2

d・f=0

d・g=0

e・f=−1/2

e・g=0

f.g=1/2

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