$0,1$-polytopse are fundamental objects in combinatorial geometry and comvex optimization. I am interested in the size of binary representation of hyperplanes to use in the framework of computational complexity theory. Let $v_1, v_2, \dots, v_N$ be points in $\{0,1\} \subseteq \mathbb{R}^n$.  Does every facet of the convex hull of these points lie on a supporting hyperplane $$\sum_{i=1}^n a_i x_i = t,$$ where every coefficient $a_i$ is either 0 or 1?If not, how many bits are needed to express the coefficients $a_i$ of a facet hyperplane?
On facets of 01-polytope
convex optimization;integer programming;convex geometry