Two-dimensional multilayer materials with an induced moiré pattern, either due to strain or relative twist between layers, provide a versatile platform for exploring strongly correlated and topological electronic phenomena. While these systems offer unprecedented tunability, their theoretical description remains challenging due to their complex atomic structures and large unit cells. A key step in constructing effective theories is determining the relevant symmetry group of these systems. Here, we use a combination of analytical methods, molecular dynamics simulations, and first-principles calculations to show that twisted atomic configurations with distinct microscopic symmetries converge to a universal moiré-scale symmetry that governs the low-energy physics. We apply this framework to three widely studied families of moiré materials—twisted bilayer graphene, twisted hexagonal boron nitride, and twisted transition metal dichalcogenides—and introduce quantitative criteria for structural and electronic equivalence grounded in numerical accuracy and experimental resolution. This emergent universality provides a robust foundation for symmetry-respecting models and offers insight into the role of commensurability in real twisted moiré systems.

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• Flat bands
• Twistronics
• Moire materials
• Density functional calculations
• Symmetries in condensed matter