2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/63388This is a survey on algorithmic questions about combinatorial and geometric properties of convex polytopes. We give a list of 35 problems; for each the current state of knowledege on its theoretical complexity status is reported. The problems are grouped into the sections ``Coordinate Descriptions'', ``Combinatorial Structure'', ``Isomorphism'', ``Optimization'', ``Realizability'', and ``Beyond Polytopes''.CombinatoricsMetric Geometry52Bxx (Primary) 68Q25 (Secondary)text