Orientable triangular embeddings of the complete graphs on 36s vertices from noncyclic current graphs

Abstract

Mark Jungerman's 1975 Ph.D. thesis presents several infinite families of index 2 current graphs that generate triangular embeddings of complete or near-complete graphs. However, there is one family mentioned, the complete graphs on $36s$ vertices, where Jungerman solves only the first case $s = 1$. We generalize this example to all $s \geq 1$.