2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/68510We construct non-constructible simplicial $d$-spheres with $d+10$ vertices and non-constructible, non-realizable simplicial $d$-balls with $d+9$ vertices for $d\geq 3$.9 pages, 3 figuresCombinatoricsGeometric Topology57Q15; 52B05; 52B22; 57M25text