■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)

  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)

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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