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I'm having troubles with searching for analytical solution of following problem. Let we work in 3-D space and have the set of points (uniform net at cube's facets):







where $h$ is const, $i=0,1,2,...,2/h,j=0,1,2,...,2/h,k=0,1,2,...,2/h$.

Let's pass in review the foolowing vectors: $(0,0,0)$ is the beginning of each vector and the end of the vector is points that was written above.

It's necessary to find formula for mimimal positive (nonnegative) value of cosine of the angle between two vectors $(a,b,c)$ and $(d,e,f)$, where $|a−d|≤h,|b−e|≤h,|c−f|≤h$ (for example, $a$ can be $d$, $d+h$ or $d−h$ only).

Const $h$ is such than $2/h$ is integer always.

And I repeat again, I'm interested in analytical solution.

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You asked an awfully similar question a while ago math.stackexchange.com/questions/142721/discrete-optimization/… –  copper.hat May 8 '12 at 19:14

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