I am looking for a package that implements facet enumeration, ie given the vertices of an \mathbb{R}^n convex polytope (3 \le n \le 5), return the list of facets with a vertex index for each.
The polytope can be assumed to be simple if that helps. Native Julia algorithms would be preferred (I am running this in a docker image but I can deal with dependencies if necessary).
Eg from
v = [[0, 0, 0], [1, 0, 0], [0, 1, 0], [0, 0, 1]] # hi I am a simplex
I would like to get
[[1, 2, 3, 4], [1, 2, 3, 4], [1, 2, 3, 4], [1, 2, 3, 4]]
in some form.