Material's geometrical structure is a fundamental part of their properties. The honeycomb geometry of graphene is responsible for the arising of its Dirac cone, while the kagome and Lieb lattice hosts flat bands and pseudospin-1 Dirac dispersion. These features seem to be particular for few 2D systems rather than a common occurrence. Given this correlation between structure and properties, exploring new geometries can lead to unexplored states and phenomena. Kepler is the pioneer of the

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... ical tiling theory, describing ways of filing the euclidean plane with geometrical forms in its book {\it Harmonices Mundi}. In this letter, we characterize $1255$ lattices composed of the euclidean plane's k-uniform tiling, with its intrinsic properties unveiled - this class of arranged tiles present high-degeneracy points, exotic quasiparticles, and flat bands as a common feature. Here, we present aid for experimental interpretation and prediction of new 2D systems.