By exploring the maximal magnetic space groups for the P 4/n crystallographic space group, it is clear that the magnetic structure of Ni 4 V 3 O 10 is not a simple commensurate phase with a magnetic propagation vector of k = 0. There are six maximal space groups: P 4/n and P 2 ′ /c ′ can be ruled out due to their ferromagnetic ordering, while P 4 ′ /n and P 4 ′ /n ′ do not allow local moments on the Ni2/V2 or V3 sites. To visualize the remaining two, magnetic moments with arbitrary and equal magnitudes are assigned to each space group based on the allowed moment directions. The first magnetic space group, P 4/n ′ , allows for a, b, and c components of the moment on Ni1/V1 and for only a c component on Ni2/V2 and V3. The other, P 2 ′ /c, splits Ni1/V1 into However, antiferromagnetic ordering is violated for both P 4/n ′ and P 2 ′ /c in Ni 4 V 3 O 10 through Ni2/V2-O-V3 bonding paths between cells along the c-axis and also through Ni1/V1-O-Ni1/V1 bonding paths within the crystallographic cell. Figure shows the spin arrangement of P 4/n ′ , and Fig. shows that of P 2 ′ /c. Oxide ions are omitted for clarity of the spin orientations. Figure includes an additional Ni2/V2 ion from the cell above and a V3 ion from the cell below. The polyhedral connections between these ions (opaque polyhedra in Fig. ) demonstrate how these connections break antiferromagnetic ordering across 180 • superexchange paths. Moreover, Fig. includes a (001) slice in the cell to illustrate the other discrepancy's location. In this slice, the opaque polyhedra in Fig. have the same spin orientations and violate antiferromagnetic ordering. Both P 4/n ′ and P 2 ′ /c contain both spin orientation issues.