Reaction of Cu₂(OH)₂CO₃ and 3-amino-1,2,4-triazole (Hatz) in aqueous ammonia under hydrothermal condition generates copper(i) triazolate with three different forms, namely α-[Cu(atz)] (1α, P2₁/c, a = 3.6325(6) Å, b = 10.284(2) Å, c = 10.481(2) Å, β = 97.379(3)°, V = 388.3(1) ų), β-[Cu(atz)] (1β, Pbca, a = 10.3115(9) Å, b = 10.498(1) Å, c = 14.744(1) Å, V = 1596.0(3) ų), and γ-[Cu(atz)] (1γ, P2₁/c, a = 8.4608(7) Å, b = 10.3198(9) Å, c = 10.5728(9) Å, β = 118.944(8)°, V = 807.8(1) ų). Structural analyses revealed that the three structures have the same chemical composition and essentially identical local and two-dimensional coordination structures, and their structural differences only arise from different packing fashions of the curved layers, which is a new mode of supramolecular isomerism in coordination polymers. The photoluminescence property of the title compound was also studied.