  The original proof of the genus of the complete graphs $K_n$ depended on
Mayer's \emph{ad hoc} solutions for $n = 18, 20, 23$. Recently, an improved
solution for $K_{20}$ was found by the author. The purpose of this note is to
use the theory of current graphs to interpret the aforementioned result and to
provide new embeddings of $K_{18}$ and $K_{23}$.
