On page 133 of Rotman's Introduction to Algebraic Topology it is stated that one requires at least 14 triangles in any triangulation of the torus.
Admittedly, I do not have a very good understanding of triangulations.
From what I understand, the following seems like a perfectly valid triangulation of the torus:
What is the mistake in this?
The NE and SW blocks both contain triangles with vertices 1,3,4. But these intersect in just the edge 13 and the vertex 4, while the intersection of two simplices in a triangulation must be a "face" of each (which might be the empty simplex), not a union of two or more simplices.