TMC tetrahedral types MOD 2k + 1 and their structure graphs

In [3,4,5], we treated edge weighted tetrahedra with a zero-sum condition on their triangles as the vertices of a graph Gi,n whose adjacency is given by the sharing of pairs ofedge-weighted triangles. In the present paper, we consider the situation modulo an odd positive integer n, so that we deal with hnite graph G'^,o. However, we are interested in a subgraph Gi.n of G;.4 that sheds light on the structure of the totally multicolored tetrahedra of complete Cayley graphs of odd orders, for Gi.n has surprising structural properties in itself.