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In this note we give a brief review of the construction of a toric variety 
$\mathcal{V}$ coming from a genus 
$g\,\ge \,2$ Riemann surface 
${{\sum }^{g}}$ equipped with a trinion, or pair of pants, decomposition. This was outlined by J. Hurtubise and L. C. Jeffrey. A. Tyurin used this construction on a certain collection of trinion decomposed surfaces to produce a variety 
$D{{M}_{g,}}$ the so-called Delzant model of moduli space, for each genus 
$g$ . We conclude this note with some basic facts about the moment polytopes of the varieties $\mathcal{V}$ . In particular, we show that the varieties 
$D{{M}_{g}}$ constructed by Tyurin, and claimed to be smooth, are in fact singular for 
$g\,\ge \,3$ .
