Edge-pairing isometries and counting Dirichlet domains on the densest tessellation 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 2 π / 3 as well as a procedure for counting the number of Dirichlet domains on the densest tessellation { 12 g − 6,3 } for signal set design with applications in space-time block codes [1].