Hierarchical classification and single-crystal X-ray analysis of unique pseudo-cubic hydrogen-bond networks composed of primary ammonium carboxylates were carried out. The networks consist of four carboxylate anions and four primary ammonium cations at the corners of the cube, and twelve charge-assisted N--H...O hydrogen bonds on the sides of the cube. The configuration of the carboxylate anions generates topological diversity in the network. The results of this hierarchical classification showed that pseudo-cubic hydrogen-bond networks composed of primary ammonium carboxylates can form nine topologically different networks. These pseudo-cubic networks are a subset of the networks formed by octameric water in the form of an "ice cube". The classification system can be applied to other pseudo-cubic networks in a similar way. A survey of crystal structures based on combinations of triphenylacetic acid with various alkylamines (carbon numbers up to eight) and examination of the CSD (Cambridge Structural Database) showed eight salts that form such networks in their crystal structures. These structures are classified into six topologically different networks. Similar networks composed of other salts are also discussed from a topological point of view.