■周期的四面体らせん構造(その22)
A(0,0,b)
B(0,0,−b)
C(0,h,0)
D(x,y,0)
E(−x,y,0)
F(α,β,γ)
AC^2=h^2+b^2=1
AD^2=x^2+y^2+b^2=1
CD^2=x^2+(y−h)^2=1
x^2+y^2−2yh+h^2=1
1−b^2−2yh+h^2=1
b^2=−2hy+h^2
y=(h^2−b^2)/2h=(2h^2−1)/2h
y^2=(2h^2−1)^2/4h^2
x^2=h^2−y^2
−b^2=x^2+y^2−1
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F(α,β,γ)の計算は以下の通りである.
△ACDの重心Gは
A(0,0,b)
C(0,h,0)
D(x,y,0)
G(x/3,(h+y)/3,b/3)
F(α,β,γ)はB+2BGで与えられる.
BG=(x/3,(h+y)/3,b/3+b)
2BG=(2x/3,2(h+y)/3,8b/3)
B+2BH=(2x/3,2(h+y)/3,5b/3)=F(α,β,γ)
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