Single crystals Of pure silica zeolite SSZ-55 were prepared using the fluoride route. Single-crystal X-ray diffraction at a synchrotron source revealed the framework structure of the material, but the unit cell (orthorhombic a = 12.905(2) angstrom, b = 21.344(4) angstrom, c = 5.1279(10)) is too small to accommodate ordered arrays of the organic structure-directing agent. Molecular modeling was used to simulate the docking of the structure-directing agent in the channels of the material, and this revealed a strong space-filling interaction with a number of possible orientations of the organic cation. The overall non-centrosymmetric structure of the solid (spacegroup C222(1)) was confirmed using second harmonic generation experiments.