■等面単体の体積(その383)

  P0(1,0,√2)

  P1(0,0,0)

  P2(1,√2,0)

  P3(2,0,0)

  P0P1=P1P2=P2P3=√3

  P0P2=P1P3=2

  P0P3=√3

 試しに

  P0(m,0,m√2,h)

  P1(0,0,0,0)

  Px(0,0,0,4h)

  P2(m,m√2,0,3h)

  P3(2m,0,0,2h)

とおくと,

  P0P1^2=3m^2+h^2

  P0Px^2=3m^2+9h^2

  P0P2^2=4m^2+4h^2

  P0P3^2=3m^2+h^2

  P1Px^2=16h^2

  P1P2^2=3m^2+9h^2

  P1P3^2=4m^2+4h^2

  PxP2^2=3m^2+h^2

  PxP3^2=4m^2+4h^2

  P2P3^2=3m^2+h^2

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[まとめ]組み合わせが複雑になりそうだ.絞り込みが必要と思われる.

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