$Z$ is an identification space of the unit square $Q=\{(x, y) | 0 \leq x, y \leq 1\}$ with the following identifications:
$(0, y)$~$(1, y)$
$(x, 0)$~$(x+ \frac{1}{2}, 0) $
$(x, 1) $~ $(x + \frac{1}{2}, 1) $
I drew the following net:
But I am unsure how to construct a triangulation. Could you help me please?