%0 Journal Article %T Euler characteristic and quadrilaterals of normal surfaces %A Tejas Kalelkar %J Mathematics %D 2008 %I arXiv %R 10.1007/s12044-008-0015-7 %X 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 $\tau$. %U http://arxiv.org/abs/0810.0174v1