Zeolites, microporous aluminosilicates, are amongst the most widely used catalysts in the petrochemical industry. Zeolite catalytic functionality is coupled to the distribution of tetrahedral alumina (AlO4-) and associated counter-cations throughout the aluminosilicate framework, yet little is definitively known about the factors that govern framework aluminium arrangement. It is generally accepted that all zeolites obey Lowensteins rule of aluminium avoidance and that Al-O-Al linkages are forbidden. Here, we describe the unprecedented screening of aluminium distribution in catalytically active zeolite SSZ-13 in both its protonated and sodium containing forms, H-SSZ-13 and Na-SSZ-13, using density functional theory. We predict violations of Lowensteins rule in high and low silica H-SSZ-13 and other protonated frameworks considered in this investigation, H-LTA, H-RHO and H-ABW. The synthetic realisation of these zeolites could spur the development of new catalytic routes and materials, and the optimisation of existing zeolite catalysts.