A classification of regular maps with Euler characteristic $-p^4$ for a prime $p\geq 5$
A map is a cellular decomposition of a closed surface. In the framework of classifying all regular maps by their supporting surface, it is an open problem to find all closed surfaces that support no regular maps. Classification of regular maps on surfaces with Euler characteristic $-p, -p^2, -p^3, -2p,$ and $-3p$ has already been done...