■格子のボロノイ細胞(その100)

【1】E6無限鏡映群の基本単体の頂点座標

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

  (1/4,1/4,1/4,1/4,1/4,−1/4,−1/4,1/4)

  (0,0,1/3,1/3,1/3,−1/3,−1/3,1/3)

  (0,0,0,1/2,1/2,−1/3,−1/3,1/3)

  (0,0,0,0,1,−1/3,−1/3,1/3)

  (−1/4,1/4,1/4,1/4,1/4,−5/12,−5/12,5/12)

  (0,0,0,0,0,−2/3,−2/3,2/3)

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【2】E6のボロノイ細胞

[1]1/2(x1+x2+・・・+x8)=1

[2]x1+x8=x2+x3+・・・+x7

[3]x1=x2

[4]x2=x3

[5]x3=x4

[6]x4=x5

[7]x1=−x2

[2]を外すと

 x1=x2=x3=x4=x5=0

 x6=x7=−2/3

 x8=2/3

[3]を外すと

 x3=x4=x5=1/4

 x1=−x2=−1/4

 x6=x7=−5/12

 x8=5/12

[4]を外すと

 x4=x5=1/3

 x1=x2=0

 x6=x7=−1/3

 x3=x8=1/3

[5]を外すと

 x5=1/2

 x1=x2=x3=0

 x6=x7=−1/3

 x3=0,x8=1/3

[6]を外すと

 x1=x2=x3=x4=0

 x6=x7=−1/3

 x5=1,x8=1/3

[7]を外すと

 x1=x2=x3=x4=x5=1/4

 x6=x7=−1/4

 x8=1/4

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【3】E6~について(222)

  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)

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