First-principles density functional calculations were used to calculate surface properties of the LiMn2O4 spinel. The calculations were benchmarked to obtain the correct semiconducting, Jahn-Teller distorted electronic ground state of bulk LiMn2O4 and, using the same parameters, the predominant low-index polar surface facets (100), (110), and (111) were calculated to study their structure and stability. Following an investigation of possible surface terminations as well as surface layer reconstructions we find that the (111) LMO surface stabilizes through a targeted site exchange of the undercoordinated surface Mn cations with fully coordinated tetrahedral subsurface Li cations, effectively creating a partial inverse spinel arrangement at the surface. This reconstruction renders the (111) facet the most stable among the investigated facets. The equilibrium (Wulff) shape of a LiMn2O4 particle was constructed and exhibits a cubo-octahedral shape with predominant (1 1 1) facets, in agreement with common experimental findings for the spinel structure.