Dynamics of regular clusters of many non-touching particles falling under gravity in a viscous fluid at low Reynolds number are analysed within the point-particle model. Evolution of two families of particle configurations is determined: 2 or 4 regular horizontal polygons (called `rings) centred above or below each other. Two rings fall together and periodically oscillate. Four rings usually separate from each other with chaotic scattering. For hundreds of thousands of initial configurations, a map of the cluster lifetime is evaluated, where the long-lasting clusters are centred around periodic solutions for the relative motions, and surrounded by regions of the chaotic scattering,in a similar way as it was observed by Janosi et al. (1997) for three particles only. These findings suggest to consider the existence of periodic orbits as a possible physical mechanism of the existence of unstable clusters of particles falling under gravity in a viscous fluid.
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