■基本単体の二面角(その104)

 (その103)の

  P1(1,0,0,0,0,0,0,0)

  P2(1/2,1/2,0,0,0,0,0,0)

  P3(2/3,1/3,1/3,0,0,0,0,0)

  P4(3/4,1/4,1/4,1/4,0,0,0,0)

  P5(4/5,1/5,1/5,1/5,1/5,0,0,0)

  P6(5/6,1/6,1/6,1/6,1/6,1/6,0,0)

  P7(5/6,1/6,1/6,1/6,1/6,1/6,1/6,1/6)

  P8(7/8,1/8,1/8,1/8,1/8,1/8,1/8,−1/8),x1+x8=x2+x3+x4+x5+x6+x7,はE6~のボロノイ細胞

  P0(0,0,0,0,0,0)

  P1(1,0,0,0,0,0)

  P2(1,1/√3,0,0,0,0)

  P3(1,1/√3,1/√3,0,0,0)

  P4(1,1/√3,1/√3,1,0,0)

  P5(1,1/√3,0,0,1/√3,0)

  P6(1,1/√3,0,0,1/√3,1)

と相同だろうか?

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  P1P2^2=1/2

  P1P3^2=1/3

  P1P4^2=1/4

  P1P5^2=1/5

  P1P6^2=1/6

  P1P7^2=8/36

  P1P8^2=1/8

  P2P3^2=2/36+1/9=1/6

  P2P4^2=1/4

  P2P5^2=18/100+3/25=3/10

  P2P6^2=2/9+4/36=1/3

  P2P7^2=2/9+1/6=1/3

  P2P8^2=18/64+6/64=3/8

どうも一致しないようだ.

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