Euler Characteristics for Generalized Tetrahedron Groups

This paper is concerned with a class of groups which generalize the ordinary tetrahedron groups. This class of groups was introduced by Fine and Rosenberger and independently by Vinberg. Some conditions for the generalized tetrahedron groups to have a rational Euler characteristic are shown here and the values of the Euler characteristics in these cases are calculated. In addition here are some geometrical applications of the Euler characteristic of generalized tetrahedron groups.^{1 2}