■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)

  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)

  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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