■サマーヴィルの等面四面体(その376)
P1(0,0,0)
P2(1/√2,√3/√2,0)
P3(2/√2,0,0)
は
P1P2=P2P3=√2
P1P3=√2
を満たす.=△2
P1(0,0,0)
P2(m/√2,m√3/√2,0)
P3(2m/√2,0,0)
は
P1P2=P2P3=m√2
P1P3=m√2
を満たす.
P0(0,0,0)
P1(0,0,3h)
P2(m/√2,m√3/√2,h)
P3(2m/√2,0,2h)
P0P1^2=9h^2
P0P2^2=2m^2+h^2
P0P3^2=2m^2+4h^2
P1P2^2=2m^2+4h^2
P1P3^2=2m^2+h^2
P2P3^2=2m^2+h^2
2m^2+h^2(3)<2m^2+4h^2(2)
9h^2(1)
G5は
P2P3=P3P4=P4P5=√5
P2P4=P3P5=√8
P2P5=3
ここで,
9h^2=9
2m^2+4h^2=8
2m^2+h^2=5,h^2=1,m^2=2
は条件を満たす.
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