■多面体のコマ(その5)
格子のボロノイ細胞V(0)に対する慣性モーメントの計算結果を示したい.
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[1]An型格子
I(V(0))=I(S)=n/12+n/6(n+1)
G(An)=1/n・I(V(0))/vol(V(0))^(2/n)
=1/(n+1)^1/n・{n/12+n/6(n+1)}
→1/12
−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−
[2]Dn型格子
G(Dn)=1/2^2/n・{1/12+1/2n(n+1)}
→1/12
−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−
[3]E型格子
G(E8)=929/12960=0.0716821
G(E7)=163/2016・2^-1/7=0.0732306
G(E6)=5/56・3^-1/6=0.0743467
−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−
[4]E*型格子
G(E6*)=12619・3^1/6/204120=0.0742437
G(E7*)=21361・2^1/7/322560=0.0731165
−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−
[5]D*型格子
G(D3*)=19/192・2^1/3
G(D4*)=13/120√2
G(D5*)=2641/23040・2^3/5=0.0756254
G(D6*)=601・2^1/3/10080=0.0751203
−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−
[6]A*型格子
G(An*)=Jn+1/n(n+1)^(1-1/n)
J1=0,J2=1/12,J3=5/18,J4=19/32
J5=389/375,J6=1045/648,J7=78077/33614
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