2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/113949Every finite, self-dual, regular (or chiral) 4-polytope of type {3,q,3} has a trivalent 3-transitive (or 2-transitive) medial layer graph. Here, by dropping self-duality, we obtain a construction for semisymmetric trivalent graphs (which are edge- but not vertex-transitive). In particular, the Gray graph arises as the medial layer graph of a certain universal locally toroidal regular 4-polytope.18 pages (to appear in Journal Combinatorial Theory, Series A)CombinatoricsMetric Geometry05C25; 51M20text