In this talk, we present some natural crystallizations of the generalized lens spaces \(L(p, q_1, \dots, q_n)\) for integers \(p\geq 2\), \(n\geq 1\) and integers \(q_1, \dots, q_n\) relatively prime to \(p\). These crystallizations are quotients of triangulations of the sphere \(S^{2n+1}\).
