The rational reticular design of metal-organic frameworks (MOFs) from building units of known geometries is essential for enriching the diversity of MOF structures. Unexpected and intriguing structures, however, can also arise from subtle changes in the rigidity/length of organic linkers and/or synthetic conditions. Herein, we report three uranium-based MOF structures—i.e., NU-135X (X = 0, 1, 2)—synthesized from trigonal planar uranyl nodes and triptycene-based hexacarboxylate ligands with variable arm lengths. A new chiral 3,6-connected nuc net was observed in NU-1350, while the extended versions of the ligand led to 3-fold catenated MOFs (NU-1351 and NU-1352) with rare 3,6-connected cml-c3 nets. The differences in the topology of NU-1350 and NU-1351/NU-1352 could be attributed to the slight distortions of the shorter linker in the former from the ideal trigonal prism geometry to an octahedral geometry when coordinated to the trigonal planar uranyl nodes.