Abstract: The aim of this work is to establish a systematic methodology for generating automatically different tessellations and double-layer grids (DLGs) following a newly defined, specific nomenclature. This particular nomenclature defines the notation of mosaics and DLGs in a synthesized and unique manner, and can generate and design them after the parameters expressed in their own names. By means of an algorithm and some computational codes, it is possible to recreate in 3D any DLGs directly from their own names. The current nomenclature for tessellations is also analyzed and found to have severe disadvantages, such as the excessive length of their notations and their nonunique character. A new nomenclature is proposed to define and generate n-uniform mosaics consistently and unequivocally in a manner consistent with the current nomenclature used for Archimedean (regular and semiregular) tessellations.

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