The Bell-Wigner polytope has the following extreme points
I checked the largest set of independent position vectors consists of 7 points thus it's a six dimensional polytope. I wanted to find all the facet inequalities. I was thinking of the following method
For each selection of six points out of the given eight points do the following : see if they are linearly independent, if they are then obtain five independent vectors from them and form the 5 dimensional hyperplane they define and check if all the extreme eight points lie on one side of this hyperplane, if yes it defines a facet.
Am I correct ? Also can any kind of symmetry or some other thing help me simplify my method ?