This study proposes an edge-based single-resolution compression scheme for triangular mesh connectivity. The proposed method improves upon EdgeBreaker. Nearly all of these algorithms are either multiple traversals or operate in reverse order. Operating in reverse order should work only off-line in the EdgeBreaker decompression process. Many restrictions on applications will be caused by these factors. To overcome these restrictions, the algorithm developed here can both encode and decode 3D models in a straightforward manner by single traversal in sequential order. Most algorithms require complicated operations when the triangular mesh is split. This study investigates spatial locality to minimize costs in split operations. Meanwhile, some simplification rules are proposed by considering geometric characteristics which ignore the last triangle when a split occurs. The proposed method improves not only the compression ratio but also the execution time.