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Application of the same pattern for linking neighbouring 4.82 two-dimensional nets as is found in the AlPO4-CJ2 and AlPO4-15 structures allows the enumeration of eleven (4;2)-connected three-dimensional nets with a maximum unit-cell repeat of ~ 10 Å. Net 551 is polytypic with net 398 (the tetrahedral analogue of AlPO4-12). The (4;2)-connected nets related to AlPO4-15 (net 400) and AlPO4-CJ2 (net 725) have the highest symmetry of the present nets. Synthetic zeolite Linde J may have the latter framework topology. Nets 400 and 725 relax considerably upon lowering of the space group symmetry. Geometrical refinements indicate that the mixed-coordinated AlPO4-15 is more feasible than its (4;2)-connected relative (same space group symmetry); the feasible net 398 and the topologically simpler net 551 have not been observed so far. Geometrically optimized atomic coordinates are given for the most feasible nets obtained here.