  The cut polytope ${\rm CUT}(n)$ is the convex hull of the cut vectors in a
complete graph with vertex set $\{1,\ldots,n\}$. It is well known in the area
of combinatorial optimization and recently has also been studied in a direct
relation with admissible correlations of symmetric Bernoulli random variables.
That probabilistic interpretation is a starting point of this work in
conjunction with a natural binary encoding of the CUT($n$). We show that for
any $n$, with appropriate scaling, all vertices of the polytope ${\mathbf
1}$-CUT($n$) encoded as integers are approximately on the line $y= x-1/2$.
