Abstract
A Dirichlet-Voronoi decomposition constructed for a regular system of points is always regular. But certain regular decompositions of the Euclidean plane into Dirichlet-Voronoi planigons, it turns out, possess still more such action center systems which are not regular systems of points. In particular, for certain regular Dirichlet-Voronoi decompositions, aperiodic action center systems have been discovered. In connection with this, an investigation is launched of all possible action center systems for each fixed regular decomposition of the Euclidean plane.
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