2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/215301We prove Gaussian approximation theorems for specific $k$-dimensional marginals of convex bodies which possess certain symmetries. In particular, we treat bodies which possess a 1-unconditional basis, as well as simplices. Our results extend recent results for 1-dimensional marginals due to E. Meckes and the author.v4: major revision incorporating recent improvements in the main technical tools. To appear in Beitraege Algebra GeomMetric GeometryProbability52A20; 60F05text