■サマーヴィルの等面四面体(その391)

 n=5の場合,

  P0(1/2,(√5)/2,0,(√10)/2)

  P1(0,0,0,0)

  P2(2,0,0,0)

  P3(3/2,(√5)/2,(√10)/2,0)

  P4(1,√5,0,0)

  P0(m/2,m√5/2,0,m√10/2,h)

  P1(0,0,0,0,0)

  P2(0,0,0,0,5h)

  P3(2m,0,0,0,4h)

  P4(3m/2,m√5/2,m√10/2,0,3h)

  P5(m,m√5,0,0,2h)

としてみる.

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  P0P1^2=4m^2+h^2

  P0P2^2=4m^2+16h^2

  P0P3^2=6m^2+9h^2

  P0P4^2=6m^2+4h^2

  P0P5^2=4m^2+h^2

  P1P2^2=25h^2

  P1P3^2=4m^2+16h^2

  P1P4^2=6m^2+9h^2

  P1P5^2=6m^2+4h^2

  P2P3^2=4m^2+h^2

  P2P4^2=6m^2+4h^2

  P2P5^2=6m^2+9h^2

  P3P4^2=4m^2+h^2

  P3P5^2=6m^2+4h^2

  P4P5^2=4m^2+h^2

(その388)

h^2=1/5,m^2=6/5はこれらを満たす.

  h^2=1/5,5h=√5  (△5の最短辺)

  m^2の値からスケーリングができる.

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