We further conducted an in-depth mathematical study of Moiré patterns to enhance the understanding of the structural properties in triangular lattices. Since Moiré patterns arise from the superposition of two MOF layers, the patterns can be decomposed into two periodic triangular lattices (Figure ). Notably, at specific twist angles, the triangular lattices within the twisted bilayer MOF strictly aligned creating a periodic superlattice, referred to as a commensurate superlattice (Figure ). Through mathematical derivation, we investigated the correlation between twist angle and aperiodicity/periodicity (see Supplementary Information Section 4 for the detailed procedure). The commensuration occurs when twist angle θ satisfies,