1. Introduction Eptar tiling (often referred to in patent and engineering literature as “Eptar®” or “EPTAR tiling”) is a proprietary tiling system developed originally for advanced composite materials, particularly in aerospace and automotive sectors. Unlike periodic tilings (e.g., squares or hexagons) or famous aperiodic tilings (Penrose), Eptar tilings are characterized by a locally irregular, globally homogenous pattern that minimizes weak planes and optimizes stress distribution.
The name “Eptar” derives from a combination of “EP” (epoxy/polymer) and “tar” (suggesting a spread layer), but in geometry, it is often linked to a seven-fold symmetry concept (Greek hepta = seven), though true seven-fold tilings are impossible in periodic Euclidean planes. 2.1 Non-periodic, non-periodic tiling class Eptar tilings belong to the class of aperiodic tilings but with a crucial difference: they are constructed using a substitution rule that generates a hierarchical structure with no translational symmetry, yet with a well-defined average coordination number. eptar tiling