Bulk photopolymerization of a library of synthesized multifunctional azides and alkynes was carried out toward developing structure–property relationships for CuAAC-based polymer networks. Multifunctional azides and alkynes were formulated with a copper catalyst and a photoinitiator, cured, and analyzed for their mechanical properties. Material properties such as the glass transition temperatures (Tg) show a strong dependence on monomer structure with Tg values ranging from 41 to 90 °C for the series of CuAAC monomers synthesized in this study. Compared to the triazoles, analogous thioether-based polymer networks exhibit a 45–49 °C lower Tg whereas analogous monomers composed of ethers in place of carbamates exhibit a 40 °C lower Tg. Here, the formation of the triazole moiety during the polymerization represents a critical component in dictating the material properties of the ultimate polymer network where material properties such as the rubbery modulus, cross-link density, and Tg all exhibit strong dependence on polymerization conversion, monomer composition, and structure postgelation.