Could you please upload your `$my_dual_sub` and `$my_signs`? One way would be to save the `$S_0` object and share the resulting JSON.

I can't promise, but maybe we can do a bit more here.

I still don't understand. Let's postpone this. Concerning your tertatoid, I think I know a way, modulo some experimenting. Here are the steps. (1) Construct the regular tetrahedron as the convex hull of every other vertex of the cube [-1,1]^3. Call this polytope T. (2) From each edge of T construct ...

What is the "perpendicular bisector" of an edge? Do you mean the affine hyperplane which is perpendicular to a given edge, passing through the midpoint of that edge? Your "tetartoid" is given without coordinates, and from the description given on that web page I cannot deduce how...

Of course, we will fix those errors in polymake. However, your specific computation can be rescued as follows: polytope > $C = new Cone(INEQUALITIES =>[[1,0,0,0,0,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0,0,0,0],[0,0,0,1,0,0,0,00,0,0,0],[0,0,0,0,1,0,0,0,0,0,0,0],[0,0,0,0,0,1,0,0,0,...

OK, so for fixed dimension d, assuming the resulting polytope to be simplicial (with prob 1) is indeed crucial for the algorithms to run in linear time? This is not what I said. Note that in the expression O(mnd) the parameter m (number of facets) depends on n (number of vertices/input points). Rou...

Indeed, polymake employs a convex hull computation to compute the vertex-facet incidences from input points. Most algorithms/implementations produce FACETS and VERTICES_IN_FACETS together. If this is not the case there is a second step to compute scalar products between each row of VERTICES and each...

Here is a question that I received: I was wondering what computational complexity I can expect from VERTICES_IN_FACETS for m vertices on the d sphere. Does it rely on a convex hull algorithm? If yes, on which? As I am using this wonderfully practicable function as a non-specialist in convex geometry...

A google search for "polymake" and "newton polytope" reveals:
https://polymake.org/doku.php/user_guid ... s_tutorial

The code of the client gc_closure can be viewed on github.

The algorithm is described in §22.3 and §23.1 of Schrijver's book on integer and linear programming (Wiley 1986).

The first description is the facet description of your input. Here it is essentially the same as your input, as the given inequalities proved to be irredundant. For an overview of how to apply polymake in the context of integer linear programming, including integer hulls, see this tutorial . More de...