2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/217195In this article we verify an orbifold version of a conjecture of Nimershiem from 1998. Namely, for every flat $n$-manifold $M$, we show that the set of similarity classes of flat metrics on $M$ which occur as a cusp cross-section of a hyperbolic $(n+1)$-orbifold is dense in the space of similarity classes of flat metrics on $M$. The set used for density is precisely the set of those classes which arise in arithmetic orbifolds.Revised after referee report. 11 pages. To appear in Geom. DedicataGeometric TopologyGroup Theorytext