2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/102045We discuss different approaches for the enumeration of triangulated surfaces. In particular, we enumerate all triangulated surfaces with 9 and 10 vertices. We also show how geometric realizations of orientable surfaces with few vertices can be obtained by choosing coordinates randomly.18 pages, 6 figuresCombinatoricsMetric Geometry57Q15; 05C30; 52B70text