In this paper we present a systematic procedure for the establishment of edge-pairing isometries in order to achieve the largest possible number (2g+1) of transformations pairing diametrically opposite edges and the angle between any two adjacent edges being equal to 2PI/3 as well as a procedure for counting the number of Dirichlet domains on the densest tessellation {12g - 6,3} for signal set design with applications in space-time block codes.