■等面単体の体積(その154)

 (その149)では

  A(0,0,0,0)

  B(1,0,0,a)

  C(1/2,√3/2,0,2a)

  D(1/2,√3/6,√6/3,3a)

  E(0,0,0,4a)

としたが,

  A(0,0,0,0)

  B(1,1,0,a)

  C(1,0,1,2a)

  D(0,1,1,3a)

  E(0,0,0,4a)

としてみる.

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  b^2=2+a^2

  c^2=2+4a^2

  d^2=2+9a^2

  4a=dとおくと,

  16a^2=2+9a^2,a^2=2/7

  b^2=16/7,c^2=22/7,d^2=32/7

  4a=cとおくと,

  16a^2=2+4a^2,a^2=1/6

  b^2=13/6,c^2=16/6,d^2=21/6

  4a=bとおくと,

  16a^2=2+a^2,a^2=2/15

  b^2=32/15,c^2=38/15,d^2=48/15

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[まとめ]いずれもNG.

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