We report the structural analysis of the highly-doped lithium fulleride Li12C60, performed using low-temperature neutron powder diffraction. Although the main reflections could be initially indexed with a fcc cell, Monte Carlo Simulated Annealing suggests an unusual monoclinic arrangement for the fullerene molecules. In this structure, C60 units with the same orientation are alternatively stacked to form layers, thus maximising their sterical crowding. Rietveld refinement allowed to localise Li ions, which are organised in clusters belonging to the pseudo-tetrahedral voids with a non-complete charge transfer as confirmed by Raman spectroscopy.