■等面単体の体積(その158)

 5次元正単体(辺の長さ1)

  (−1/2,−√3/6,−√6/12,−√10/20,−√15/30)

  (+1/2,−√3/6,−√6/12,−√10/20,−√15/30)

  (0,√3/3,−√6/12,−√10/20,−√15/30)

  (0,0,√6/4,−√10/20,−√15/30)

  (0,0,0,0,√10/5,−√15/30)

  (0,0,0,0,0,√15/6)

を平行移動させる

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

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

  C(1/2,√3/2,0,0,0,2a)

  D(1/2,√3/6,√6/3,0,0,3a)

  E(1/2,√3/6,√6/3,√10/4,0,4a)

  F(1/2,√3/6,√6/3,√10/4,√15/5,5a)

  G(0,0,0,0,0,6a)

  b^2=1+a^2

  c^2=1+4a^2

  d^2=1+9a^2

  e^2=1+16a^2

  f^2=1+25a^2

  6a=fとおくと,

  36a^2=1+25a^2,a^2=1/11

  b^2=12/11,c^2=15/11,d^2=20/11,e^2=27/11,f^2=36/11

  6a=eとおくと,

  36a^2=1+16a^2,a^2=1/20

  b^2=21/20,c^2=24/20,d^2=29/20,e^2=36/20,f^2=45/20

  6a=dとおくと,

  36a^2=1+9a^2,a^2=1/27

  b^2=28/27,c^2=31/27,d^2=36/27,e^2=43/27,f^2=52/27

  6a=cとおくと,

  36a^2=1+4a^2,a^2=1/32

  b^2=33/32,c^2=36/32,d^2=41/32,e^2=48/32,f^2=57/32

  6a=bとおくと,

  36a^2=1+a^2,a^2=1/35

  b^2=36/35,c^2=39/35,d^2=44/35,e^2=51/35,f^2=60/35

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