The information storage and encoding ability of DNA arise from a remarkably simple 4--letter -A, T, G, C nucleobase code. Expanding this DNA 'alphabet' provides information about its function and evolution, and introduces new functionalities into nucleic acids and organisms. Previous efforts relied on the synthetically demanding incorporation of non--canonical bases into nucleosides. Here we report the discovery that a small molecule, cyanuric acid, with three thymine--like faces reprograms the assembly of unmodified poly(adenine) into stable, long and abundant fibers with a unique internal structure. Poly(A) DNA, RNA and PNA all form these assemblies. Our studies are consistent with the association of adenine and cyanuric acid units into a hexameric rosette, bringing together poly(A) triplexes with subsequent cooperative polymerization. Fundamentally, this study shows that small hydrogen--bonding molecules can be used to induce the assembly of nucleic acids in water, leading to new structures from inexpensive and readily available materials.