The reaction of M(II) ions with azido ligands in the presence of different amino carboxylic acids gave four three-dimensional metal-azido coordination polymers, [Mn(3,5-daba)(N(3))](n) (1), [Cd(3,5-daba)(N(3))](n) (2; 3,5-daba = 3,5-diaminobenzoate), [Mn(4-aba)(N(3))](n) (3; 4-aba = 4-aminobenzoate), and [Cu(2)(gly)(2)(N(3))(2)](n) (4; gly = glycinate), which display different topological structures. Polymers 1 and 2 present 4,6-connected 3D networks with different Schlafli symbols. However, 3 and 4 feature an unprecedented trinodal 3,6-connected network with the Schlafli symbol (4(2).6)(4.6(2))(4(3).6(6).8(6)) and an unusual 4-connected 3D net with the Lonsdaleite (hexagonal diamond) topology, respectively. Magnetic susceptibility measurements revealed dominant antiferromagnetic couplings for 1 and 3 and an overall dominant ferromagnetic coupling for 4, which presents metamagnetic behavior with a magnetic phase transition at a critical temperature of 6 K and a transition field of ca. 6030 Oe. The results demonstrate that the EE azido and syn-anti carboxylato bridges in our cases induce an antiferomagnetic interaction, and the anti-anti carboxylato bridge in 4 mediates a ferromagnetic interaction. The magnetic interaction through the EO azido bridge in 3 and 4 has a dependence on the value of the M-N-M bond angle.