If "0 >= -1" occurs as a facet, then your polyhedron is necessarily unbounded. The converse, by the way, is not true. The thing is that combinatorially polymake treats all polyhedra as bounded polytopes (with a marked face at infinity, which may have any dimension). This has a number of al...

There are several things to consider then: (1) If you pass float coordinates as point coordinates of a Polytope object, then they will be converted to exact rationals automatically. (2) In general, there is no way (known) to "approximately" compute convex hulls with floats throughout. In d...

(1)Is it safe to simply cast the Rational scalar to a double for further usage in my application? In general: no. Rational is an exact type, double is not. If a conversion makes sense or not will depend on what you want to compute. Usually, you just want to stick with Rational. polymake supports ar...

A few more remarks: (1) Specifying polytopes in terms of a V-description works by providing POINTS. Using VERTICES is potentially more efficient, but this requires that the points (i.e., rows of the matrix) are actually, the vertices, and without repetitions. (2) We use a homogeneous coordinate mode...

In addition to what Ewgenij said, you will need to make sure that the executable polymake-config is in your path.

You were right: the documentation in polymake was lacking. I added a short comment with a reference to our paper. This will appear in the next release.

So, thank you for helping to make polymake better.

Our implementation is slightly more general than primitive patchworking; it covers what is sometimes is called "combinatorial patchworking" in the literature. This means, we require that the lattice points (@my_monomials in your case) correspond to the entire set of monomials in, say, n va...

We did make changes concerning threejs in order to obtain correct visualization for https://www.matchthenet.de/xmas. And I can confirm your problem.

Requires an investigation. Stay tuned.

That does not have unique solutions. Instead the set of such solutions forms a polyhedron in the parameter space (= coefficients of the linear combinations).

Sorry, I don't understand the question.

Is it that P_2 is a subpolytope of P_1, and you want to find those vcertices of P_1 which are not vertices of P_2?