nprofile1qyt8wumn8ghj7un9d3shjtnyd968gmewwp6kytcqyqscmj9x6m32fy8njlxrhyctj7lg2nhauw22pg42mpnqvsmzx33ag6ml4xy (nprofile…l4xy) I have not used Mathematica, but I have used Polymake to generate the equations of the facets of a polytope from the set of vertices. The polytopes I've examined mostly have (0,1) vertices. Note that Polymake uses homogenous coordinates, so I've added an \( x_0 \) term to the vertices, and the output has an \( x_0 \) term instead of a constant term.
https://polymake.org/doku.php/start