On pg. 133 of Rotman's Introduction to Algebraic Topology, we have a figure 
which claims to be a triangulation of the torus.
Now a triangulation of a topological space is defined as
Definition. A triangulation of a topological space $X$ is a finite simplicial complex $K$ (in some Euclidean space) along with a homeomorphism $h:|K|\to X$.
I interpret the picture as a simplicial complex $K$ whose members are each of the little triangles along with all their edges and vertices. To claim that the given figure is a triangulation, we need to produce a homeomorphism $h:|K|\to T$, where $T$ denotes the torus.
One way to give a map from $|K|$ to $T$ is by seeing $T$ as the quotient space formed by identifying the left and the right edges and the top and the bottom edges (the usual way of making a torus from a rectangular piece of paper), and having the map $h:|K|\to T$ as the quotient map.
But this quotient map is not a homeomorphism since it is not a bijection.
I must be missing something obvius.
Best Answer
Here on this picture some simplexes are identified. When you give names to different vertices, it will look as follows