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

Timothy Sun

Published 2018-03-30, updated 2018-05-09Version 2

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