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Through analysis of variable-temperature neutron powder-diffraction data, we present solutions for the magnetic structures of ${\mathrm{SrMn}}_{7}{\mathrm{O}}_{12}$, ${\mathrm{CdMn}}_{7}{\mathrm{O}}_{12}$, and ${\mathrm{PbMn}}_{7}{\mathrm{O}}_{12}$ in all long-range ordered phases. The three compounds were found to have magnetic structures analogous to that reported for ${\mathrm{CaMn}}_{7}{\mathrm{O}}_{12}$. They all feature a higher-temperature lock-in phase with commensurate magneto-orbital coupling …