■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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