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We herein reported the syntheses, crystal structures, and magnetic properties of a two-dimensional coordination polymer {[CoII(TPT)2/3(H2O)4][CH3COO]2·(H2O)4}n (1) and a chain compound {[CoII(TPT)2(CHOO)2(H2O)2]}n (2) based on the 2,4,6-Tris(4-pyridyl)-1,3,5-triazine (TPT) ligand. Structure analyses showed that complex 1 had a cationic hexagonal framework structure, while 2 was a neutral zig-zag chain structure with different distorted octahedral coordination environments. Magnetic measurements revealed that both complexes exhibit large easy-plane magnetic anisotropy with the zero-field splitting parameter D = 47.7 and 62.1 cm−1 for 1 and 2, respectively. This magnetic anisotropy leads to the field-induced slow magnetic relaxation behaviour. However, their magnetic dynamics are quite different; while complex 1 experienced a dominating thermally activated Orbach relaxation at the whole measured temperature region, 2 exhibited multiple relaxation pathways involving direct, Raman, and quantum tunneling (QTM) processes at low temperatures and Orbach relaxation at high temperatures. The present complexes enlarge the family of framework-based single-ion magnets (SIMs) and highlight the significance of the structural dimensionality to the final magnetic properties.