A new Cd(II) coordination polymer [Cd4(μ3-OH)2(L)2(H2O)3]n (1) is constructed from an unexplored non-planar trigonal tricarboxyl ligand 3,4-bi(4-carboxyphenyl)-benzoic acid (H3L), which exhibits an unusual (4,10)-connected (3.45)(34.49.512.617.72.8) topological net based on the tetranuclear [Cd4(μ3-OH)2] secondary building units (SBUs). The elaborate modification of organic tectons provides a new perspective on the design and synthesis of highly-connected coordination networks. Additionally, the thermal stability and luminescence of the crystalline material have also been investigated.