Around right-angled hyperbolic polytopes

We will consider a class of polytopes which can be realized in a hyperbolic space with all dihedral angled equal to $\pi/2$. Since this class contains fullerene polytopes, we will describe fullerene graphs with maximal Wiener index. We will discuss combinatorics and volumes of right-angles polytopes, construction of 3-manifolds from right-angled blocks, and knots and links related to such manifolds.
Talk is based on joint works with A. Dobrynin [1] and A. Egorov [2,3].
[1] A. Dobrynin, A. Vesnin, On the Wiener Complexity and the Wiener Index of Fullerene Graphs, Mathematics, 2019, 7(11), 1071, 16 pp.
[2] A. Egorov, A. Vesnin, Volume estimates for right-angled hyperbolic polyhedra, preprint arXiv:2010.11147, 12pp.
[3] A. Egorov, A. Vesnin, On correlation of hyperbolic volumes of fullerenes with their properties, submitted, 24 pp.