I am not quite sure I understand simplicial comlexes/triangulations.
For instance, I think that the below image represents a triangulation for the 2-torus. Am I correct?
2026-03-25 06:10:25.1774419025
Is this a triangulation for the 2-torus?
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The "2-torus" usually means "the thing that looks like the surface of a donut, and is topologically the product $S^1 \times S^1$ of a circle with itself. I think you've got a triangulation of a "2-holed torus".
Certainly it looks as if it's an OK triangulation. The usual problem people get into is trying to find triangulations with very few triangles/vertices, and they end up with two different triangles that have the same three vertices, for instance.
Yours has a fine enough "mesh" that it looks as if that cannot happen, and (assuming you've got the arrows on the edges oriented properly -- I didn't check -- it appears to me to be fine.