Five indium(III) compounds with 2,5-pyridine dicarboxylate ligands: {[4,4′-Hbipy] [In(Hpdc)(H2O)Cl3]·2H2O}n (1), {[4,4′-H2bipy]4[In2(pdc)7(H2O)]·7H2O}n (2), {[4,4′-H2bipy]3 [In2(pdc)6(H2O)]·6H2O}n (3), {[In2(pdc)2(bpno)(H2O)2Cl2]·2H2O}n (4) and [In2(pdc)2(2,2′-bipy)Cl2]n (5), (H2pdc = 2,5-pyridine-dicarboxylic acid, 4,4′-bipy = 4,4′-bipyridine, bpno = 4,4′-bipyridine N,N-dioxide, 2,2′-bipy = 2,2′-bipyridine) were hydrothermally or solvothermally synthesized and their structures were determined by X-ray single-crystal diffraction. Compounds 1 and 2 are both mononuclear structures, which are assembled into 3-D supramolecular structures by various hydrogen bonding; compound 3 consists of two types of infinite 1-D indium(III)-carboxylate chains; compound 4 is a 2-D wave-like plane structure formed by bpno linked indium(III)-carboxylate chains. An unprecedented 3-D chiral framework of compound 5 with three kinds of helices along [010] direction is observed, considering that the construction of a chiral structure by rigid achiral ligands is rare. A topological analysis using TOPOS4.0 indicates that compound 5 is a unique and novel example of self-penetrated (4,8)-connected binodal lattice with a {32.64}{34.44.58.69.72.8} Schläfli symbol. The above-mentioned compounds were also characterized by X-ray powder diffraction (XRD), thermal gravity analysis (TGA) and photoluminescent studies.