Symmetry Groups and Fundamental Tilings for the Compact Surface of Genus 3− 2. The normalizer diagram with classification

This is a continuation of [16] where the complete diagram of metric normalizers of the fundamental groupG= ⊗ in Isom H will be determined (Table 2). Thus we completely classify the symmetry groups N/G of the 3− surface, i.e. the connected sum of 3 projective planes, into 12 normalizer classes, up to topological equivariance, by the algorithm for fundamental domains, developed in [9], [10], [11] and [15], aided by computer. Our algorithm is applicable for any compact surface with exponential complexity by the genus g.