Which version of polymake are you using? We just released version 3.3, and there it works. It is possible that in some older versions the types get messed up. Beware that the property POINTS takes a small object of type Matrix<TropicalNumber<Min>>. Object of type Rational should automatically conver...

My purpose is to compute a cone $c pointed at some vertex $v of a polytope $p, such that its rays are the affine hull of the facets of $p incident to $v, and such that $p itself is not contained in $c. Sorry, I do not understand what you want to compute. Do you want to compute the intersection of t...

Thanks for letting us now (and mentioning polymake). I like the Sierpinksi pattern!

I looked into this, but I cannot reproduce your error. Sorry. Please install a version of polymake on your system, cf. https://polymake.org/doku.php/download/start . The shell.polymake.org version has a number of limitations and is proof-of-concept only. For instance, there is an upper limit on the ...

Your input needs to be homogenized.

I'm getting errors of the form ERROR: no matching overloaded instance of... a lot, and I'm not sure how to interpret them. To give a bit more context: polymake supports operator overloading and polymorphism. That is, the function to be called is not only determined by the name of the function but a...

OK, I did one test with your example.
So cplex seems to be right about the LP.

In the meantime, assuming you have access to an MIP solver (and therefore an LP solver) at your end that can read in the files I provided in the OP, I would be really grateful if any of the polymake developers can verify if the discrepancy exists on 3.2. My OP is detailed enough to be able to repli...

Please recall that projecting a polytope down by one dimension might (asymptotically) square the number of facets. Loosing nine dimension this might result in an enormous number of facets. As a side comment: exploiting the reverse is the idea behind the so-called "extended formulations"; see, e.g., ...

If you replace what obviously needs to be replaced in $p = new Polytope(INEQUALITIES=>{non-negativity constraints}, EQUATIONS=>{three hyperplanes}); print $p->LATTICE_POINTS; then this should do the trick. Several caveats: (1) depending on your hyperplanes the result may be unbounded. (2) Deciding w...