The self-assembly of silver(I) salts with bitopic triazole ligands 4-(salicylideneamino)-1,2,4-triazole (L-1) and 4-(2-pyridinyl)-1,2,4-triazole (L-2) produced dinuclear complexes and a 1D molecular-ladder coordination polymer, while the reaction of tritopic ligand 4-(3-pyridinyl)-1,2,4-triazole (L-3) with AgClO4 afforded a right-handed helical 2D network with (4,4) topology, a meso layer constructed via left- and right-handed helical chains with AgBF4, and a 2D 4.8(2) net containing no helical chain with AgNO3. Using a tetratopic triazole ligand 2,6-bis(4-triazolyl)pyridine (L-4), a 3D coordination polymer was isolated. This complex contains a cationic 4.6(3) network with rhombic channels, accepting two columns of uncoordinated ClO4- anions filling into every central cavity. Our results show that (i) the increase of coordination sites of the ligands is an effective route to obtaining higher-dimensional structures and (ii) anions could influence the configuration of the ligand to tune the coordination network topology from those with helical chains to those without. In the solid state, all of the complexes exhibit strong fluorescent emission bands, which may be assigned to intraligand fluorescent emission. The luminescent properties of these complexes in a water solution varied from blue light to green light at ambient temperature.