I'd recommend the following two books. In the first one there are some connections to toric varieties.

<cite authors="De Loera, Jesús A.; Rambau, Jörg; Santos, Francisco">_De Loera, Jesús A.; Rambau, Jörg; Santos, Francisco_, [**Triangulations. Structures for algorithms and applications**](http://dx.doi.org/10.1007/978-3-642-12971-1), Algorithms and Computation in Mathematics 25. Berlin: Springer (ISBN 978-3-642-12970-4/hbk; 978-3-642-12971-1/ebook). xiii, 535&nbsp;p. (2010). [ZBL1207.52002](https://zbmath.org/?q=an:1207.52002).</cite>

<cite authors="Aurenhammer, Franz; Klein, Rolf; Lee, Der-Tsai">_Aurenhammer, Franz; Klein, Rolf; Lee, Der-Tsai_, [**Voronoi diagrams and Delaunay triangulations**](http://dx.doi.org/10.1142/8685), Hackensack, NJ: World Scientific (ISBN 978-981-4447-63-8/hbk). viii, 337&nbsp;p. (2013). [ZBL1295.52001](https://zbmath.org/?q=an:1295.52001).</cite>