■サマーヴィルの等面四面体(その378)
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)
H6は
P3P4=P4P5=P5P6=√6
P3P5=P4P6=√10
P3P6=√12
ここで,
9h^2=12
2m^2+4h^2=10
2m^2+h^2=6,h^2=4/3,m^2=7/3
は条件を満たす.
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