■基本単体の二面角(その384)

 SPLAG

【1】Anのボロノイ細胞

[1]-x0+xn=1

[2]x0=x1

[3]x1=x2

[4]x2=x3

[5]xn-1=xn

[2]を外すと

 x1=x2=x3=・・・=xn-1=xn=1/(n+1)

 x0=-n/(n+1)

[3]を外すと

 x0=x1=-(n-1)/(n+1)

 x2=x3=・・・=xn-1=xn=2/(n+1)

[5]を外すと

 x0=x1=・・・=xn-1=-1/(n+1)

 xn=n/(n+1)

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【2】Dnのボロノイ細胞

[1]xn-1+xn=1

[2]x1=-x2

[3]x1=x2

[4]x2=x3

[5]xn-1=xn

[2]を外すと

 x1=x2=x3=・・・=xn-1=xn=1/2

 (1/2,1/2,1/2,1/2)

[3]を外すと

 x1=-x2=-1/2

 x3=x4=・・・=xn-1=xn=1/2

 (-1/2,1/2,1/2,1/2)

[4]を外すと

 x1=x2=0

 x3=x4=・・・=xn-1=xn=1/2

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

[5]を外すと

 x0=x1=・・・=xn-1=0

 xn=1

 (0,0,0,1)

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 (1,1,1,1)

 (-1,1,1,1)

 (0,0,1,1)

 (0,0,0,2)

はD4格子と一致.

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