Caveats: 1) Note that if you are using the browser-based polymake like me (http://polymake.org/doku.php/boxdoc) you can copy from my stuff and paste into the browser by right-clicking. Be careful though because your browser/clipboard may insert line breaks, which mess it up for a big entry. Paste into notepad first and remove them. 2) I left the prompt “polytope >” in. Remove this. 3) Underscores like in F_VECTOR get removed sometimes and need replaced. Can be done in the pasting box in polymake. 4) The output below for VERTICES_IN_FACETS gives lists of the vertices, numbered 0-24, based on the order they were entered. To see one of the 5d facets, you can go back and get those vertices from the original input, and make a new polytope with just those! This also is basically a proof that vertices in their facets is enough info to get the polytope. (Considering that you can see intersections too.) 5) I put the initial “1” in each point. polytope > $points=new Matrix([[1,18,1,1,7],[1,54,1,1,7],[1,54,1,1,21],[1,54,1,3,21],[1,54,3,1,21],[1,54,3,3,21],[1,7,1,1,18],[1,7,1,1,54],[1,21,1,1,54],[1,21,1,3,54],[1,21,3,1,54],[1,21,3,3,54],[1,1,18,7,1],[1,1,54,7,1],[1,1,54,21,1],[1,1,54,21,3],[1,3,54,21,1],[1,3,54,21,3],[1,1,7,18,1],[1,1,7,54,1],[1,1,21,54,1],[1,3,21,54,1],[1,1,21,54,3],[1,3,21,54,3],[1,18,6,2,1],[1,54,6,2,1],[1,54,18,2,1],[1,54,18,6,1],[1,54,18,6,3],[1,18,6,1,2],[1,54,6,1,2],[1,54,18,1,2],[1,54,18,1,6],[1,54,18,3,6],[1,18,2,6,1],[1,54,2,6,1],[1,54,2,18,1],[1,54,6,18,1],[1,54,6,18,3],[1,18,1,6,2],[1,54,1,6,2],[1,54,1,18,2],[1,54,1,18,6],[1,54,3,18,6],[1,6,18,1,2],[1,6,54,1,2],[1,18,54,1,2],[1,18,54,1,6],[1,18,54,3,6],[1,6,18,2,1],[1,6,54,2,1],[1,18,54,2,1],[1,18,54,6,1],[1,18,54,6,3],[1,6,2,18,1],[1,6,2,54,1],[1,18,2,54,1],[1,18,6,54,1],[1,18,6,54,3],[1,6,1,18,2],[1,6,1,54,2],[1,18,1,54,2],[1,18,1,54,6],[1,18,3,54,6],[1,2,18,1,6],[1,2,54,1,6],[1,2,54,1,18],[1,6,54,1,18],[1,6,54,3,18],[1,2,6,1,18],[1,2,6,1,54],[1,2,18,1,54],[1,6,18,1,54],[1,6,18,3,54],[1,2,1,18,6],[1,2,1,54,6],[1,2,1,54,18],[1,6,1,54,18],[1,6,3,54,18],[1,2,1,6,18],[1,2,1,6,54],[1,2,1,18,54],[1,6,1,18,54],[1,6,3,18,54],[1,1,18,2,6],[1,1,54,2,6],[1,1,54,2,18],[1,1,54,6,18],[1,3,54,6,18],[1,1,6,2,18],[1,1,6,2,54],[1,1,18,2,54],[1,1,18,6,54],[1,3,18,6,54],[1,1,2,18,6],[1,1,2,54,6],[1,1,2,54,18],[1,1,6,54,18],[1,3,6,54,18],[1,1,2,6,18],[1,1,2,6,54],[1,1,2,18,54],[1,1,6,18,54],[1,3,6,18,54]]); polytope > $p=new Polytope(POINTS=>$points); polytope > print $p->F_VECTOR; 104 210 134 28 polytope > $points=new Matrix([[1,1,7,1,4],[1,1,4,1,7],[1,7,1,4,1],[1,4,1,7,1],[1,3,7,1,2],[1,7,1,2,3],[1,1,2,3,7],[1,2,3,7,1],[1,3,2,1,7],[1,2,1,7,3],[1,1,7,3,2],[1,7,3,2,1],[1,7,3,1,2],[1,3,1,2,7],[1,1,2,7,3],[1,2,7,3,1],[1,7,2,1,3],[1,2,1,3,7],[1,1,3,7,2],[1,3,7,2,1],[1,1/2,7,1,4],[1,1/2,4,1,7],[1,7,1/2,4,1],[1,4,1/2,7,1],[1,3,7,1/2,2],[1,7,1/2,2,3],[1,1/2,2,3,7],[1,2,3,7,1/2],[1,3,2,1/2,7],[1,2,1/2,7,3],[1,1/2,7,3,2],[1,7,3,2,1/2],[1,7,3,1/2,2],[1,3,1/2,2,7],[1,1/2,2,7,3],[1,2,7,3,1/2],[1,7,2,1/2,3],[1,2,1/2,3,7],[1,1/2,3,7,2],[1,3,7,2,1/2],[1,1,7,1/2,4],[1,1,4,1/2,7],[1,7,1,4,1/2],[1,4,1,7,1/2],[1,3,7,1/2,2/2],[1,7,1/2,2/2,3],[1,1/2,2/2,3,7],[1,2/2,3,7,1/2],[1,3,2/2,1/2,7],[1,2/2,1/2,7,3],[1,1/2,7,3,2/2],[1,7,3,2/2,1/2],[1,7,3,1/2,2/2],[1,3,1/2,2/2,7],[1,1/2,2/2,7,3],[1,2/2,7,3,1/2],[1,7,2/2,1/2,3],[1,2/2,1/2,3,7],[1,1/2,3,7,2/2],[1,3,7,2/2,1/2],[1,1/2,7,1/2,4],[1,1/2,4,1/2,7],[1,7,1/2,4,1/2],[1,4,1/2,7,1/2],[1,3/2,7,1/2,2/2],[1,7,1/2,2/2,3/2],[1,1/2,2/2,3/2,7],[1,2/2,3/2,7,1/2],[1,3/2,2/2,1/2,7],[1,2/2,1/2,7,3/2],[1,1/2,7,3/2,2/2],[1,7,3/2,2/2,1/2],[1,7,3/2,1/2,2/2],[1,3/2,1/2,2/2,7],[1,1/2,2/2,7,3/2],[1,2/2,7,3/2,1/2],[1,7,2/2,1/2,3/2],[1,2/2,1/2,3/2,7],[1,1/2,3/2,7,2/2],[1,3/2,7,2/2,1/2],[1,1/2,7,1/2,4/2],[1,1/2,4/2,1/2,7],[1,7,1/2,4/2,1/2],[1,4/2,1/2,7,1/2],[1,3/2,7/2,1/2,2/2],[1,7/2,1/2,2/2,3/2],[1,1/2,2/2,3/2,7/2],[1,2/2,3/2,7/2,1/2],[1,3/2,2/2,1/2,7/2],[1,2/2,1/2,7/2,3/2],[1,1/2,7/2,3/2,2/2],[1,7/2,3/2,2/2,1/2],[1,7/2,3/2,1/2,2/2],[1,3/2,1/2,2/2,7/2],[1,1/2,2/2,7/2,3/2],[1,2/2,7/2,3/2,1/2],[1,7/2,2/2,1/2,3/2],[1,2/2,1/2,3/2,7/2],[1,1/2,3/2,7/2,2/2],[1,3/2,7/2,2/2,1/2],[1,1/2,7/2,1/2,4/2],[1,1/2,4/2,1/2,7/2],[1,7/2,1/2,4/2,1/2],[1,4/2,1/2,7/2,1/2]]); polytope > $p=new Polytope(POINTS=>$points); polytope > print $p->F_VECTOR; 104 210 134 28