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Kollros' Theorem

For every ring containing $p$ Spheres, there exists a ring of $q$ Spheres, each touching each of the $p$ Spheres, where

\begin{displaymath}
{1\over p}+{1\over q}={1\over 3}.
\end{displaymath}

The Hexlet is a special case with $p=3$.

See also Hexlet, Sphere


References

Honsberger, R. Mathematical Gems II. Washington, DC: Math. Assoc. Amer., p. 50, 1976.




© 1996-9 Eric W. Weisstein
1999-05-26