I am trying to understand the triangulation of a projective plane and it has been proven that minimally we need six points to triangulate.
But I do not understand why a rectangle above (using 3 points) is not a triangulation. From what I know, triangulation has to be simplicial complex. In the diagram, opposite points A and B have been identified.
Can anyone explain to me in a way that is easiest to understand? Because I am really a beginner to this.
For that rectangle to be a projective plane, you need each of the four tringular cells in the picture to be distinct cells. I guess you imagine the edges of the triangles identified as the labes indicate, but still having four cells in the end. That is a more general structure called CW-complex, and in that context you have more flexible ways for "gluing" cells.
In the context of simplicial complexes, you can only have one $2$-simplex with vertices $A, B, C$, so that figure doesn't make sense as a simplicial complex. (Recall that every simplex is completely determined by its vertices!)
I hope that helps!