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([[1,1,0,0,0,0,0],[1,0,1,0,0,0,0],[1,0,0,1,0,0,0],[1,0,0,0,1,0,0],[1,0,0,0,0,1,0],[1,0,0,0,0,0,1],[1,1,1,0,0,0,0],[1,1,0,0,1,0,0],[1,1,0,0,0,1,0],[1,1,0,0,0,0,1],[1,0,1,1,0,0,0],[1,0,1,0,1,0,0],[1,0,1,0,0,0,1],[1,0,0,1,1,0,0],[1,0,0,1,0,1,0],[1,0,0,1,0,0,1],[1,0,0,0,1,1,0],[1,0,0,0,0,1,1],[1,1,1,0,1,0,0],[1,1,1,0,0,0,1],[1,0,1,1,1,0,0],[1,0,0,1,1,1,0],[1,1,0,0,0,1,1],[1,0,0,1,0,1,1],[1,0,0,0,0,0,0]]); polytope > \$p=new Polytope(POINTS=>\$points); polytope > print \$p->F_VECTOR; 25 93 142 111 48 11 polytope > print \$p->VERTICES_IN_FACETS; {0 1 2 4 5 6 8 9 10 12 14 15 17 19 22 23 24} {10 12 15 19 20 23} {0 2 3 4 5 7 8 9 13 14 15 16 17 21 22 23 24} {1 2 3 4 5 10 11 12 13 14 15 16 17 20 21 23 24} {7 8 16 18 21 22} {0 1 2 3 4 6 7 8 10 11 13 14 16 18 20 21 24} {3 5 7 9 11 12 13 15 16 17 18 19 20 21 22 23} {1 4 6 8 10 11 12 14 16 17 18 19 20 21 22 23} {0 1 2 3 5 6 7 9 10 11 12 13 15 18 19 20 24} {0 1 3 4 5 6 7 8 9 11 12 16 17 18 19 22 24} {0 2 6 7 8 9 10 13 14 15 18 19 20 21 22 23}