2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/71441L. Paoluzzi constructed a family of compact orientable three-dimensional hyperbolic manifolds with totally geodesic boundary, which were, by construction, closely related to the three-dimensional torus. This paper gives their complete classification up to isometry, and also their isometry groups. The key tool is the so-called canonical decomposition of hyperbolic manifolds.13 pages, 6 figuresGeometric Topology57M50; 57M60A classification of hyperbolic manifolds related to the three-dimensional torustext