  Let $M$ be a compact 3-manifold with a triangulation $\tau$. We give an
inequality relating the Euler characteristic of a surface $F$ normally embedded
in $M$ with the number of normal quadrilaterals in $F$. This gives a relation
between a topological invariant of the surface and a quantity derived from its
combinatorial description. Secondly, we obtain an inequality relating the
number of normal triangles and normal quadrilaterals of $F$, that depends on
the maximum number of tetrahedrons that share a vertex in $\tau$.
