Many industrially important materials, ranging from ceramics to catalysts to pharmaceuticals, are polycrystalline and cannot be grown as single crystals. This means that non-conventional methods of structure analysis must be applied to obtain the structural information that is fundamental to the understanding of the properties of these materials. Electron microscopy might appear to be a natural approach, but only relatively simple structures have been solved by this route. Powder diffraction is another obvious option, but the overlap of reflections with similar diffraction angles causes an ambiguity in the relative intensities of those reflections. Various ways of overcoming or circumventing this problem have been developed, and several of these involve incorporating chemical information into the structure determination process. For complex zeolite structures, the FOCUS algorithm has proved to be effective. Because it operates in both real and reciprocal space, phase information obtained from high-resolution transmission electron microscopy images can be incorporated directly into this algorithm in a simple way. Here we show that by doing so, the complexity limit can be extended much further. The power of this approach has been demonstrated with the solution of the structure of the zeolite TNU-9 (|H9.3|[Al9.3Si182.7O384]; ref. 10) with 24 topologically distinct (Si,Al) atoms and 52 such O atoms. For comparison, ITQ-22 (ref. 11), the most complex zeolite known to date, has 16 topologically distinct (Si,Ge) atoms.