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DNA double helices containing metal-mediated DNA (mmDNA) base pairs are constructed from Ag+ and Hg2+ ions between pyrimidine:pyrimidine pairs with the promise of nanoelectronics. Rational design of mmDNA nanomaterials is impractical without a complete lexical and structural description. Here, the programmability of structural DNA nanotechnology toward its founding mission of self-assembling a diffraction platform for biomolecular structure determination is explored. The tensegrity triangle is employed to build a comprehensive structural library of mmDNA pairs via X-ray diffraction and generalized design rules for mmDNA construction are elucidated. Two binding modes are uncovered: N3-dominant, centrosymmetric pairs and major groove binders driven by 5-position ring modifications. Energy gap calculations show additional levels in the lowest unoccupied molecular orbitals (LUMO) of mmDNA structures, rendering them attractive molecular electronic candidates.