■等面単体の体積(その156)

 4次元正単体(辺の長さ1)

  (−1/2,−√3/6,−√6/12,−√10/20)

  (+1/2,−√3/6,−√6/12,−√10/20)

  (0,√3/3,−√6/12,−√10/20)

  (0,0,√6/4,−√10/20)

  (0,0,0,0,√10/5)

を平行移動させる

  A(0,0,0,0,0)

  B(1,0,0,0,a)

  C(1/2,√3/2,0,0,2a)

  D(1/2,√3/6,√6/3,0,3a)

  E(1/2,√3/6,√6/3,√10/4,4a)

  F(0,0,0,0,5a)

  b^2=1+a^2

  c^2=1+4a^2

  d^2=1+9a^2

  e^2=1+16a^2

  5a=eとおくと,

  25a^2=1+16a^2,a^2=1/9

  b^2=10/9,c^2=13/9,d^2=2,e^2=25/9

  5a=dとおくと,

  25a^2=1+9a^2,a^2=1/16

  b^2=17/16,c^2=20/16,d^2=25/16,e^2=2

  5a=cとおくと,

  25a^2=1+4a^2,a^2=1/21

  b^2=22/21,c^2=25/21,d^2=30/21,e^2=37/21

  5a=bとおくと,

  25a^2=1+a^2,a^2=1/24

  b^2=25/24,c^2=28/24,d^2=31/24,e^2=40/24

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