A new single-sheeted DMBE potential energy surface for ground-state C₃ is reported. The novel analytical form accurately describes the three symmetry-equivalent C_2v disjoint seams, in addition to the symmetry-required D_3h one, over the entire configuration space. The present formalism warrants by built-in construction the confluence of the above crossings, and the rotation-in-plane of the C_2v seams when the perimeter of the molecule fluctuates. Up to 1050 ab initio energies have been employed in the calibration procedure, of which 421 map the loci of intersection. The calculated energies have been scaled to account for the incompleteness of the basis set and truncation of the MRCI expansion, and fitted analytically with chemical accuracy. The novel form is shown to accurately mimic the region defined by the 4 conical intersections, while exhibiting similar attributes to the previously reported one [J. Chem. Phys., 2015, 143, 074302] at the regions of configuration space away from the crossing seams. Despite being mainly addressed to C₃, the present approach should be applicable to adiabatic PESs of any X₃ system experiencing similar topological attributes, in particular the small-linear-parameter Jahn–Teller molecules.