Let $M$ be a convex subset of the unit hypercube embedded in $\mathbb{R}^n$ as
$$ 0 \le x_1 ... x_n \le 1 $$
With the property that $M$ is the convex hull of its vertices, and all of its vertices are integer points lying on the corners of the unit hypercube.
It is easy then to define a notion of a "binary dual" of $M$, $M'$ where $M'$ is a convex hull of all the vertices of the hypercube that are not in $M$.
A concrete example, Given:
$$M: x -y =0, 0 \le y \le 1 $$
As such a $M$ in $\mathbb{R}^2$ we can find its binary dual to be:
$$ M': x +y =1, 0 \le x \le 1 $$
Which can be verified by drawing the two structures out and checking that $M'$ has vertices strictly where $M$ does not.
So that leads to a natural question, given the $H$ representation of $M$ (so it arrives as a collection of inequalities) which you are told is the convex hull of its binary integer vertices, how does one efficiently compute $M'$ (as a collection of inequalities)?