Abstract
The triangulation of a convex polytope is one of the most important topics in the classical theory of convex polytopes. In this chapter the modern treatment of triangulations of convex polytopes is systematically developed. In Section 4.1 we recall fundamental materials on convex polytopes and summarize basic facts without their proofs. The highlight of Chapter 4 is Section 4.2, where unimodular triangulations of convex polytopes are introduced and studied in the frame of initial ideals of toric ideals of convex polytopes. Furthermore, the normality of convex polytopes is discussed. Finally, in Section 4.3, we study the Lawrence lifting of a configuration, which is a powerful tool for computing the Graver basis of a toric ideal. Furthermore, unimodular polytopes, which form a distinguished subclass of the class of normal polytopes, are discussed.
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Herzog, J., Hibi, T., Ohsugi, H. (2018). Convex Polytopes and Unimodular Triangulations. In: Binomial Ideals. Graduate Texts in Mathematics, vol 279. Springer, Cham. https://doi.org/10.1007/978-3-319-95349-6_4
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