Is this a triangulation of a cylinder?

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I am currently a beginner in Algebraic topology. I don't know whether triangulations of a thing are unique or not. So I thought to ask here whether the "triangulation" I've come up with is really a triangulation or not?

I am currently a beginner in Algebraic topology. I don't know whether triangulations of a thing are unique or not. So I thought to ask here whether the "triangulation" I've come up with is really a triangulation or not?

I've shaded the triangles to show 2-simplexes.

P.S.- I have posted this question from the app and I'm trying to make the image horizontal.