Résumé : We discuss the characterization of $(f_0, f_1)$-pairs of $d$-polytopes for $d=3, 4, 5$. We completely characterize the $(f_0, f_1)$-pairs of $6$-dimension polytopes and find a characterization of $7$-dimension polytopes having excess degree greater than 11. We finally conjecture bounds fulfilled by $d$-polytopes with excess greater than $3d-10$.
[Slides.pdf] [arXiv] [vidéo]
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