[show abstract][hide abstract] ABSTRACT: Porous materials such as zeolites contain well-defined pores in molecular dimensions and have important industrial applications in catalysis, sorption and separation. Aluminosilicates with intersecting 10- and 12-ring channels are particularly interesting as selective catalysts. Many porous materials, especially zeolites, form only nanosized powders and some are intergrowths of different structures, making structure determination very challenging. Here, we report the atomic structures of an aluminosilicate zeolite family, ITQ-39, solved from nanocrystals only a few unit cells in size by electron crystallography. ITQ-39 is an intergrowth of three different polymorphs, built from the same layer but with different stacking sequences. ITQ-39 contains stacking faults and twinning with nano-sized domains, being the most complex zeolite ever solved. The unique structure of ITQ-39, with a three-dimensional intersecting pairwise 12-ring and 10-ring pore system, makes it a promising catalyst for converting naphtha into diesel fuel, a process of emerging interest for the petrochemical industry.