Dune morphology was simulated using coupled models of wind flow and sand transport for 4728 tri-directional wind regimes and bed conditions. The dominant control of dune morphology is sand coverage on the bed. Dunes on a fully sand-covered bed tend to form a periodic pattern of long crests with a relatively uniform spacing. In contrast, dunes on a starved bed have greater diversity of crest orientations and shapes, including complex shapes that have not been simulated or observed in bidirectional wind regimes. These specific dune shapes resulting from the tri-directional wind regime persist regardless of whether the transport capacity of the weakest wind is comparable to or only 1/10th that of the dominant wind. On sand-covered beds, dunes generally have only a single modal orientation (approximately that with maximum gross bedform-normal transport). The exceptions are where two strong winds diverge by 90° (two dune orientations arise), where three winds have triradial symmetry (three dune orientations), or winds have modest deviations from triradial symmetry (two dune orientations). On a starved bed, increasing the divergence angle between two strong winds produces a highly generalized sequence of: barchan dunes (divergence angle ∼30° between the two dominant winds), squat barchans or domes (divergence angle of ∼60°), dunes with two or three crest orientations (divergence angles ∼90° or 120°), to slug-shaped or boomerang-shaped dunes (divergence angle 180°, i.e., reversing winds). The simulated morphologies include a wide variety of Martian dune shapes, which allows their formative wind regimes to be inferred.