The (0001) surface of vanadium sesquioxide, V₂O₃, is terminated by vanadyl groups under standard ultra high vacuum preparation conditions. Reduction with electrons results in a chemically highly active surface with a well-defined LEED pattern indicating a high degree of order. In this work we report the first quantitative structure determination of a reduced V₂O₃(0001) surface. We identify two distinct surface phases by STM, one well ordered and one less well ordered. I/V-LEED shows the ordered phase to be terminated by a single vanadium atom per surface unit cell on a quasi-hexagonal oxygen layer with three atoms per two-dimensional unit cell. Furthermore we compare the method of surface reduction via electron bombardment with the deposition of V onto a vanadyl terminated film. The latter procedure was previously proposed to result in a structure with three surface vanadium atoms in the 2D unit cell and we confirm this with simulated STM images.