Edge-pairing isometries and counting Dirichlet domains on the densest tessellation {12g−6,3} for signal set design

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 2π/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 [1].