We highlight fast Li-ion diffusion in hypothetical tetragonal Li10GeP2O12 (LGPO), as a counterpart to the well-known phases of orthorhombic (LISICON) LGPO, thio-LISICON, and tetragonal Li10GeP2S12 (LGPS). We use extended Car-Parrinello molecular dynamics in the canonical and isobaric-isothermal ensembles, finding first that tetragonal LGPO is dynamically stable, albeit 0.04 Ha/f.u. above LISICON LGPO. The calculated activation energy for Li-ion diffusion is 0.22 eV, well below the value calculated for LISICON LGPO (0.34 eV), and similar to those for thio-LISICON (0.23 eV) and tetragonal LGPS (0.18 eV). These results indicate that hypothetical tetragonal LGPO, although less stable than its orthorhombic allotrope, shows a room-temperature conductivity comparable to LGPS, and, if synthesized, could make a very attractive Li-ion conductor.