  We study groups generated by three half-turns in the Lobachevsky $3$-space
and their quotient orbifolds. These generalized triangle groups are closely
related to the arbitrary 2-generator Kleinian groups. Our main result is a
classification of the singular sets of the generalized triangle orbifolds. We
also present a method to obtain the parameters defining a generalized triangle
group from the structure of the singular set of its quotient orbifold and
illustrate it by examples.
