Won't you always be able to put a slightly larger atom if you let the atom move up or down out of the trigonal plane? Anyway, it sounds like you are asking for the largest circle which fits in the hole between three circles who are touching (this is a 2D problem?). Try a google for "Descartes Circle Theorem" for 2D or "Soddy Circles" for nD. An answer can even be found at the fountain of all human knowledge:
        http://en.wikipedia.org/wiki/Descartes%27_theorem

Best,

Jon

Jean-Noel Chotard wrote:
Dear all,

I'm facing a geometrical problem which I hope will be obvious for some of you. How can we calculate the maximum atomic radius of an intersitial trigonal site formed by 3 different atoms? Does anybody know a mathematical way to do so or maybe even a software which could calculate that?

Thank you.

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