■格子と多面体(その15)
【1】An無限鏡映群の基本単体の頂点座標
V0(0^n+1)
V1(−n/(n+1),(1/(n+1))^n)
V2((−(n−1)/(n+1))^2,(2/(n+1))^n-1)
Vn((−1/(n+1))^n,n/(n+1))
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【2】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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