Dihedral Branches Coverings of Hyperbolic Orbifolds

Abstract

We consider the class of hyperbolic 3-orbifolds whose underlying topological space is the 3-sphere S3 and whose singular set is a trivalent graph with singular index 2 along each edge (an important special case occurs when the trivalent graph is the 1-skeleton of a hyperbolic polyhedron). Our main result is a classification of the D-branched coverings of these orbifolds (where D2 is the dihedral group of order 4) under some general conditions on their isometry groups or the lengths of their geodesics.