Irregular triangulations of complete graphs on 12s vertices in orientable surfaces

Abstract

We present a family of index 1 abelian current graphs whose derived embeddings can be modified into triangulations of $K_{12s}$ for $s\ge 4$. Our construction is significantly simpler than previous methods for finding genus embeddings of $K_{12s}$, which utilized either large index or nonabelian groups.

7 pages, 4 figures