Some generalized Coxeter groups and their orbifolds

Abstract

In this note we construct examples of geometric 3-orbifolds with (orbifold) fundamental group isomorphic to a ($\mathbb{Z}$-extension of a) generalized Coxeter group. Some of these orbifolds have either euclidean spherical or hyperbolic structure. As an application we obtain an alternative proof of theorem 1 of Hagelberg, Maclaughlan and Rosenberg in [5]. We also obtain a similar result for generalized Coxeter groups.