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Posted: **24 Apr 2025, 23:10**

Although I thought it will be something trivial, I cannot find how to obtain the hyperplane representation of a polyhedron given by its vertices. Polymake use lrs, and it is very easy there, so must be here too.

What I have tried:

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$p = new Polytope(POINTS=>[[1,0,0,0],[1,8,0,0],[1,9,0,3],[1,9,3,0],[1,0,12,0],[1,0,0,12]]);
print $p->INEQUALITIES;

which gives an error, but no inequalities in compressed form. However, I can print the constraints like this:

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print_constraints($p);

But I need it in matrix form instead. How can I get that?

Thanks in advance!

Posted: **05 May 2025, 07:29**

You can get the inequalities (or more precisely the facets) in matrix form via:

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print $p->FACETS;

INEQUALITIES is an input property to supply possibly redundant inequalities while FACETS can be computed to give a proper H-description of the polytope.

Some more details are explained in this tutorial about polytopes: https://polymake.org/doku.php/user_guid ... s_polytope

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