Minimal fragmentation models intend to unveil the statistical properties oflarge ensembles of identical objects, each one segmented in {\it two} partsonly. Contrary to what happens in the multifragmentation of a single body,minimally fragmented ensembles are often amenable to analytical treatments,while keeping key features of multifragmentation. In this work we present astudy on the minimal fragmentation of regular polygonal plates with up to $100$sides. We observe in our model the typical statistical behavior of a solidteared apart by a strong impact, for example. That is to say, a robust powerlaw, valid for several decades, in the small mass limit. In the present case wewere able to analytically determine the exponent of the accumulated massdistribution to be $\frac{1}{2}$. Less usual, but also reported in a number ofexperimental and numerical references on impact fragmentation, is the presenceof a sharp crossover to a second power-law regime, whose exponent we found tobe $\frac{1}{3}$ for an isotropic model and $\frac{2}{3}$ for a more realisticanisotropic model.
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