where m and n are coprime integers and |𝑚 -𝑛| mod 3 ≠ 0 (Figure ). The mathematical relationship is analogous to that of the twisted bilayer graphene, despite differences in the lattice structure (the triangular lattice of this MOF system and the hexagonal lattice of graphene) (Figure ). In addition, the continuous Moiré patterns could be demonstrated by the Moiré period (λ), representing the distance between successive repetitions of the interference pattern (Figures 3B and S16 where aMOF is the lattice constant of MOFs (corresponding to the inter-cluster distance; 1.7, 1.9, and 2.1 nm for Zr-NDC, Zr-BPDC, and Zr-AZDC). Note that the lattice constants of Zr-MOFs differ significantly from that of graphene (0.246 nm), ranging from 85.5 to 88.3% for Zr-NDC to Zr-AZDC. The λ diverges in incommensurate angles. As the twist angle increases, the Moiré period decreases, also corroborated by all TEM data of Figures and. Figures and Table present the relationship between commensurate twist angle (θ) and Moiré period (λ) for the three MOFs. Consequently, the Moiré pattern with a twist angle of 30 degrees corresponds to an aperiodic structure as this angle cannot be expressed by defined criteria involving m and n (Figures ).