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This work reports the results of studying the magnetic properties of two novel sodium nickel phosphates representing the rare case of Ni2+-based magnetic systems with dominating FM interactions. Na5Ni2(PO4)3H2O (I) and Na6Ni2(PO4)3OH (II) are quasi-one-dimensional FM showing two different exchange topologies: the spin chain and spin ladder, respectively. The temperature dependence of magnetic susceptibility of Na5Ni2(PO4)3H2O does not show any anomalies down to 2 K, while the temperature dependence of specific heat measured down to 1.8 K exhibits a clear hump at 4 K indicating the low-dimensional character of magnetic system. Exchange couplings obtained from ab initio calculations reveal two leading FM interactions, J1 = - 21 K and J2 = - 9 K, within the Ni1-Ni2 zigzag chain. Weak AFM interactions between the FM chains does not lead to a long-range magnetic order down to at least 2 K, implying TN/|J1| < 0.1, thus suggesting a more pronounced 1D than in any other FM spin-chain compound of Ni2+ reported to date. The Na6Ni2(PO4)3OH experiences the AFM magnetic ordering at 2.65 K. Ab initio calculations and fitting of the experimental data evidence for forming FM dimers along rung of spin ladder with J1 = - 5 K within the dimers, while the AFM interactions J2 = 15 K between the FM dimers lead to an overall AFM order below 2.5 K in zero field. The observed in both compounds unusual magnetic behavior is dictated by the peculiarities of crystal structure. Specifically, the FM interaction J2 observed in Na5Ni2(PO4)3H2O at 106.4o of Ni2+-L-Ni2+ bridging angle is well above the crossover value, which according to the Goodenough-Kanamori-Anderson (GKA) rules is 96o. Even more surprisingly, J2 in Na6Ni2(PO4)3OH is only weakly AFM, despite the fact that the bridging angle exceeds the crossover value by 24o. These imply that the FM nature of J2 is enhanced through additional structural features beyond the Ni-O-Ni links. The PO4 bridges may play the role by creating additional superexchange pathways not accounted for by the GKA rules.