Molecular and crystalline structures of (BH 3 ) n have been theoretically studied in the pressure regime from 1 atm to 100 GPa. At lower pressures, crystals of the familiar molecular dimer are the structure of choice. At 1 atm, in addition to the well-characterized β diborane structure, we suggest a new polymorph of B 2 H 6 , fitting the diffraction lines observed in the very first X-ray diffraction investigation of solid diborane, that of Mark and Pohland in 1925. We also find a number of metastable structures for oligomers of BH 3 , including cyclic trimers, tetramers, and hexamers. While the higher oligomers as well as one-dimensional infinite chains (bent at the bridging hydrogens) are less stable than the dimer at ambient pressure, they are stabilized, for reasons of molecular compactness, by application of external pressure. Using periodic DFT calculations, we predict that near 4 GPa a molecular crystal constructed from discrete trimers replaces the β diborane structure as the most stable phase and remains as such until 36 GPa. At higher pressures, a crystal of polymeric, one-dimensional chains is preferred, until at least 100 GPa.