Settling the genus of the $n$-prism

In a 1977 paper, Ringel conjectured a formula for the genus of the $n$-prism $K_n\times K_2$ and verified its correctness for about five-sixths of all values $n$. We complete this calculation by showing that, with the exception of $n=9$, Ringel’s conjecture is true for $n\equiv 5,9(\mathrm{m}\mathrm{o}\mathrm{d}12)$.