Triangulations of the Torus (Example 4 from Munkres' Chapter 1.3)

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Below it is possible to find an extract from Chapter 1.3 of Munkres' "Elements of Algebraic Topology", which concerns the triangulation of the torus.

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I have the following question regarding Figure 3.5: do we really need $af$, $fh$, $hj$, and $ja$?
Indeed, I have in mind other triangulations of the torus where all these segments are missing.

Every feedback will be (more than) greatly appreciated, since I find all this truly impenetrable.

Thank you for your time!