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One challenge in supramolecular chemistry is the design of versatile, self-assembling building blocks to attain total control of arrangement of matter at a molecular level. We have achieved reliable prediction and design of the three-dimensional structure of artificial RNA building blocks to generate molecular jigsaw puzzle units called tectosquares. They can be programmed with control over their geometry, topology, directionality, and addressability to algorithmically self-assemble into a variety of complex nanoscopic fabrics with predefined periodic and aperiodic patterns and finite dimensions. This work emphasizes the modular and hierarchical characteristics of RNA by showing that small RNA structural motifs can code the precise topology of large molecular architectures. It demonstrates that fully addressable materials based on RNA can be synthesized and provides insights into self-assembly processes involving large populations of RNA molecules.