  While 2-dimensional quantum systems are known to exhibit non-permutation,
braid group statistics, it is widely expected that quantum statistics in
3-dimensions is solely determined by representations of the permutation group.
This expectation is false for certain 3-dimensional systems, as was shown by
the authors of ref. [1,2,3]. In this work we demonstrate the existence of
``cyclic'', or $Z_n$, {\it non-permutation group} statistics for a system of n
> 2 identical, unknotted rings embedded in $R^3$. We make crucial use of a
theorem due to Goldsmith in conjunction with the so called Fuchs-Rabinovitch
relations for the automorphisms of the free product group on n elements.
