A closed orientable triangulated surface is "nice" if its
vertices can be assigned 4 colours in such a way that all 4
colours are used in the closed star of each edge. The
4-colouring can be interpreted as a simplicial map from the
surface to the 4-vertex 2-sphere. If the surface has genus
$(n-1)^2$, then the degree of this map is at least
$n^2$. Conversely we show that, if $n$ is not divisible by 2
and 3, then there are "nice" surfaces of genus $(n-1)^2$ for
which the degree of the above map is exactly $n^2$. Complex
analytically "nice" surfaces can be viewed as minimally
triangulated meromorphic functions of a Riemann surface.