CAVEATS ------------------------------------ 1) Note that if you are using the browser-based polymake like me (http://shell.polymake.org/) 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) I put the required initial “1” in each point. ------------------------------------ INPUT/OUTPUT n = 5 ------------------------------------ polytope > $points=new Matrix([[1,1,0,0,0,1,0,0,1,0,1],[1,1,0,0,0,1,0,0,0,1,0],[1,0,1,0,0,0,0,0,0,1,0],[1,0,1,0,0,0,0,0,1,0,1],[1,1,0,0,0,0,1,0,0,0,1],[1,1,0,0,0,0,0,1,0,0,0],[1,0,0,1,0,0,0,0,0,0,1],[1,0,0,0,1,0,0,0,0,0,0]]); polytope > $p=new Polytope(POINTS=>$points); polytope > print $p->F_VECTOR; 8 26 45 45 26 8 polytope > print_constraints($p); Facets: 0: x6 >= 0 1: x7 >= 0 2: -x7 - x9 - x10 >= -1 3: -x6 - x8 + x10 >= 0 4: x5 >= 0 5: x8 >= 0 6: -x5 + x8 + x9 >= 0 7: x9 >= 0 Affine hull: 0: x4 + x7 + x9 + x10 = 1 1: x1 + 1/4 x4 - x5 - x6 - 3/4 x7 + 1/4 x9 + 1/4 x10 = 1/4 2: 1/3 x1 + x2 + 1/3 x4 + 2/3 x5 - 1/3 x6 - x8 - 2/3 x9 + 1/3 x10 = 1/3 3: 1/2 x1 + 1/2 x2 + x3 + 1/2 x4 + 1/2 x6 + 1/2 x8 - 1/2 x10 = 1/2 ------------------------------------------------------------------------- n=6 ------------------------------------------------------------------------- polytope > $points=new Matrix([[1,1,0,0,0,0,1,0,0,0,1,0,0,1,0,1],[1,1,0,0,0,0,1,0,0,0,1,0,0,0,1,0],[1,1,0,0,0,0,1,0,0,0,0,1,0,0,0,1],[1,1,0,0,0,0,1,0,0,0,0,0,1,0,0,0],[1,1,0,0,0,0,0,1,0,0,0,0,0,1,0,1],[1,1,0,0,0,0,0,1,0,0,0,0,0,0,1,0],[1,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[1,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0],[1,0,1,0,0,0,0,0,0,0,1,0,0,1,0,1],[1,0,1,0,0,0,0,0,0,0,1,0,0,0,1,0],[1,0,1,0,0,0,0,0,0,0,0,1,0,0,0,1],[1,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0],[1,0,0,1,0,0,0,0,0,0,0,0,0,1,0,1],[1,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0],[1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1],[1,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0]]); polytope > $p=new Polytope(POINTS=>$points); polytope > print $p->F_VECTOR; 16 98 327 681 944 897 588 262 76 13