2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/99250We show that the size of a minimal simplicial cover of a polytope $P$ is a lower bound for the size of a minimal triangulation of $P$, including ones with extra vertices. We then use this fact to study minimal triangulations of cubes, and we improve lower bounds for covers and triangulations in dimensions 4 through at least 12 (and possibly more dimensions as well). Important ingredients are an analysis of the number of exterior faces that a simplex in the cube can have of a specified dimension and volume, and a characterization of corner simplices in terms of their exterior faces.17 pages, related work at http://www.math.hmc.edu/~su/papers.htmlCombinatoricsMetric Geometry52B11 (Primary); 52B12, 52B05 (Secondary)text