4 problems

Let $P\subset N_\mathbb{R}$ be an $n$-dimensional polytope whose dual polytope $P^*$ is a smooth projective lattice polytope in $M_\mathbb{R}$. Generalized Ewald conjecture. Then…

Let a UT-free monotone polytope be a monotone polytope with the UT-free property, and let a USFP be a unimodular smooth Fano polytope. UT-free monotone polytope conjecture. UT-free…

Let $P\subset N_R\cong\mathbb{R}^n$ be an $n$-dimensional smooth Fano polytope, meaning that $P$ is simplicial and the vertices of every facet form a basis of the lattice $N$. Ewal…

Let $P$ be a $d$-dimensional smooth Fano polytope with $n$ vertices, where $n\ge 3d-k$ and $k\le\tfrac{d}{3}$. Let $P_6$ denote the six-dimensional smooth Fano polytope used in the…