------------------------------------ CAVEATS ------------------------------------ 1) Note that if you are using the browser-based polymake like me (http://polymake.org/doku.php/boxdoc) or (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) The output below for VERTICES_IN_FACETS gives lists of the vertices, numbered 0-14, based on the order they were entered. The pictures with the numbering 0-14 are here: http://www.math.uakron.edu/~sf34/bme_faces.pdf To see one of the 4d facets, you can go back and get those vertices from the original input, and make a new polytope with just those! For an example, see the facet from {0 2 3 4 7 14} here: http://www.math.uakron.edu/~sf34/bme_faces.pdf 5) The points here are integers via multiplying the usual ones by 8. I put the initial “1” in each point. ------------------------------------ INPUT/OUTPUT ------------------------------------ ------- n=5 ------- polytope > \$points=new Matrix([[1,1,2,1,4,2,4,1,2,2,1],[1,1,2,4,1,2,1,4,2,2,1],[1,1,4,2,1,1,2,4,2,1,2],[1,1,1,2,4,4,2,1,2,1,2],[1,1,1,4,2,4, 1,2,1,2,2],[1,1,4,1,2,1,4,2,1,2,2],[1,2,1,4,1,2,2,2,1,4,1],[1,8/3,4/3,8/3,4/3,4/3,4/3,8/3,8/3,8/3,4/3],[1,2,1,1,4,2,2,2,4,1,1],[1,4/3,4/3,8/ 3,8/3,8/3,8/3,4/3,4/3,8/3,4/3],[1,4/3,8/3,4/3,8/3,8/3,8/3,4/3,4/3,4/3,8/3],[1,4,1,2,1,1,2,1,2,4,2],[1,4,2,1,1,2,1,1,2,2,4],[1,8/3,4/3,4/3,8/ 3,4/3,8/3,4/3,8/3,8/3,4/3],[1,2,2,2,2,1,1,4,4,1,1],[1,2,2,2,2,1,4,1,1,4,1],[1,4/3,8/3,8/3,4/3,8/3,4/3,8/3,4/3,4/3,8/3],[1,4/3,8/3,8/3,4/3,4/ 3,8/3,8/3,4/3,8/3,4/3],[1,4,1,1,2,1,1,2,4,2,2],[1,8/3,4/3,4/3,8/3,8/3,4/3,4/3,8/3,4/3,8/3],[1,8/3,4/3,8/3,4/3,8/3,4/3,4/3,4/3,8/3,8/3],[1,2, 2,2,2,4,1,1,1,1,4],[1,8/3,8/3,4/3,4/3,4/3,8/3,4/3,4/3,8/3,8/3],[1,8/3,8/3,4/3,4/3,4/3,4/3,8/3,8/3,4/3,8/3],[1,2,4,1,1,2,2,2,1,1,4],[1,4/3,4/ 3,8/3,8/3,8/3,4/3,8/3,8/3,4/3,4/3],[1,4/3,8/3,4/3,8/3,4/3,8/3,8/3,8/3,4/3,4/3]]); polytope > \$p=new Polytope(POINTS=>\$points); polytope > print \$p->F_VECTOR; 27 165 310 210 40 ------- n=6 ------- polytope > \$inequalities=new Matrix ([[-16,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0],[-16,1,0,0,0,0,1,1,1,1,0,0,0,0,0,0],[-16,0,1,0,0,0,1,0,0,0,1,1,1,0,0,0],[-16,0,0,1,0,0,0,1,0,0,1,0,0,1,1,0],[-16,0,0,0,1,0,0,0,1,0,0,1,0,1,0,1],[-16,0,0,0,0,1,0,0,0,1,0,0,1,0,1,1],[16,-1,-1,-1,-1,-1,0,0,0,0,0,0,0,0,0,0],[16,-1,0,0,0,0,-1,-1,-1,-1,0,0,0,0,0,0],[16,0,-1,0,0,0,-1,0,0,0,-1,-1,-1,0,0,0],[16,0,0,-1,0,0,0,-1,0,0,-1,0,0,-1,-1,0],[16,0,0,0,-1,0,0,0,-1,0,0,-1,0,-1,0,-1],[16,0,0,0,0,-1,0,0,0,-1,0,0,-1,0,-1,-1],[-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[-1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0],[-1,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0],[-1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0],[-1,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0],[-1,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0],[-1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0],[-1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0],[-1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0],[-1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0],[-1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0],[-1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0],[-1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0],[-1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0],[-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1],[8,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[8,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0],[8,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0],[8,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0],[8,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0],[8,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0],[8,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0],[8,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0],[8,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0],[8,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0],[8,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0],[8,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0],[8,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0],[8,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0],[8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1],[16,-1,-1,0,0,0,-1,0,0,0,0,0,0,0,0,0],[16,-1,0,-1,0,0,0,-1,0,0,0,0,0,0,0,0],[16,-1,0,0,-1,0,0,0,-1,0,0,0,0,0,0,0],[16,-1,0,0,0,-1,0,0,0,-1,0,0,0,0,0,0],[16,0,-1,-1,0,0,0,0,0,0,-1,0,0,0,0,0],[16,0,-1,0,-1,0,0,0,0,0,0,-1,0,0,0,0],[16,0,-1,0,0,-1,0,0,0,0,0,0,-1,0,0,0],[16,0,0,-1,-1,0,0,0,0,0,0,0,0,-1,0,0],[16,0,0,-1,0,-1,0,0,0,0,0,0,0,0,-1,0],[16,-1,-1,0,0,0,-1,0,0,0,0,0,0,0,0,0],[16,-1,0,-1,0,0,0,-1,0,0,0,0,0,0,0,0],[16,0,-1,-1,0,0,0,0,0,0,-1,0,0,0,0,0],[16,-1,0,0,-1,0,0,0,-1,0,0,0,0,0,0,0],[16,0,-1,0,-1,0,0,0,0,0,0,-1,0,0,0,0],[16,0,0,-1,-1,0,0,0,0,0,0,0,0,-1,0,0],[16,0,0,0,-1,-1,0,0,0,0,0,0,0,0,0,-1],[16,-1,0,0,0,-1,0,0,0,-1,0,0,0,0,0,0],[16,0,-1,0,0,-1,0,0,0,0,0,0,-1,0,0,0],[16,0,0,-1,0,-1,0,0,0,0,0,0,0,0,-1,0],[16,0,0,0,-1,-1,0,0,0,0,0,0,0,0,0,-1],[8,1,-1,0,0,0,-1,0,0,0,0,0,0,0,0,0],[8,1,0,-1,0,0,0,-1,0,0,0,0,0,0,0,0],[8,1,0,0,-1,0,0,0,-1,0,0,0,0,0,0,0],[8,1,0,0,0,-1,0,0,0,-1,0,0,0,0,0,0],[8,-1,1,0,0,0,-1,0,0,0,0,0,0,0,0,0],[8,0,1,-1,0,0,0,0,0,0,-1,0,0,0,0,0],[8,0,1,0,-1,0,0,0,0,0,0,-1,0,0,0,0],[8,0,1,0,0,-1,0,0,0,0,0,0,-1,0,0,0],[8,-1,0,1,0,0,0,-1,0,0,0,0,0,0,0,0],[8,0,-1,1,0,0,0,0,0,0,-1,0,0,0,0,0],[8,0,0,1,-1,0,0,0,0,0,0,0,0,-1,0,0],[8,0,0,1,0,-1,0,0,0,0,0,0,0,0,-1,0],[8,-1,0,0,1,0,0,0,-1,0,0,0,0,0,0,0],[8,0,-1,0,1,0,0,0,0,0,0,-1,0,0,0,0],[8,0,0,-1,1,0,0,0,0,0,0,0,0,-1,0,0],[8,0,0,0,1,-1,0,0,0,0,0,0,0,0,0,-1],[8,-1,0,0,0,1,0,0,0,-1,0,0,0,0,0,0],[8,0,-1,0,0,1,0,0,0,0,0,0,-1,0,0,0],[8,0,0,-1,0,1,0,0,0,0,0,0,0,0,-1,0],[8,0,0,0,-1,1,0,0,0,0,0,0,0,0,0,-1],[8,-1,-1,0,0,0,1,0,0,0,0,0,0,0,0,0],[8,0,0,0,0,0,1,-1,0,0,-1,0,0,0,0,0],[8,0,0,0,0,0,1,0,-1,0,0,-1,0,0,0,0],[8,0,0,0,0,0,1,0,0,-1,0,0,-1,0,0,0],[8,-1,0,-1,0,0,0,1,0,0,0,0,0,0,0,0],[8,0,0,0,0,0,-1,1,0,0,-1,0,0,0,0,0],[8,0,0,0,0,0,0,1,-1,0,0,0,0,-1,0,0],[8,0,0,0,0,0,0,1,0,-1,0,0,0,0,-1,0],[8,-1,0,0,-1,0,0,0,1,0,0,0,0,0,0,0],[8,0,0,0,0,0,-1,0,1,0,0,-1,0,0,0,0],[8,0,0,0,0,0,0,-1,1,0,0,0,0,-1,0,0],[8,0,0,0,0,0,0,0,1,-1,0,0,0,0,0,-1],[8,-1,0,0,0,-1,0,0,0,1,0,0,0,0,0,0],[8,0,0,0,0,0,-1,0,0,1,0,0,-1,0,0,0],[8,0,0,0,0,0,0,-1,0,1,0,0,0,0,-1,0],[8,0,0,0,0,0,0,0,-1,1,0,0,0,0,0,-1],[8,0,0,0,0,0,-1,-1,0,0,1,0,0,0,0,0],[8,0,0,0,0,0,0,0,0,0,1,-1,0,-1,0,0],[8,0,0,0,0,0,0,0,0,0,1,0,-1,0,-1,0],[8,0,-1,0,-1,0,0,0,0,0,0,1,0,0,0,0],[8,0,0,0,0,0,-1,0,-1,0,0,1,0,0,0,0],[8,0,0,0,0,0,0,0,0,0,-1,1,0,-1,0,0],[8,0,0,0,0,0,0,0,0,0,0,1,-1,0,0,-1],[8,0,-1,0,0,-1,0,0,0,0,0,0,1,0,0,0],[8,0,0,0,0,0,-1,0,0,-1,0,0,1,0,0,0],[8,0,0,0,0,0,0,0,0,0,-1,0,1,0,-1,0],[8,0,0,0,0,0,0,0,0,0,0,-1,1,0,0,-1],[8,0,0,-1,-1,0,0,0,0,0,0,0,0,1,0,0],[8,0,0,0,0,0,0,-1,-1,0,0,0,0,1,0,0],[8,0,0,0,0,0,0,0,0,0,-1,-1,0,1,0,0],[8,0,0,0,0,0,0,0,0,0,0,0,0,1,-1,-1],[8,0,0,-1,0,-1,0,0,0,0,0,0,0,0,1,0],[8,0,0,0,0,0,0,-1,0,-1,0,0,0,0,1,0],[8,0,0,0,0,0,0,0,0,0,-1,0,-1,0,1,0],[8,0,0,0,0,0,0,0,0,0,0,0,0,-1,1,-1],[8,0,0,0,-1,-1,0,0,0,0,0,0,0,0,0,1],[8,0,0,0,0,0,0,0,-1,-1,0,0,0,0,0,1],[8,0,0,0,0,0,0,0,0,0,0,-1,-1,0,0,1],[8,0,-1,-1,0,0,0,0,0,0,1,0,0,0,0,0],[8,0,0,0,0,0,0,0,0,0,0,0,0,-1,-1,1]]); polytope > \$p=new Polytope(INEQUALITIES=>\$inequalities); polytope > print \$p->N_VERTICES; 2335 polytope > print \$p->F_VECTOR; 2335 25230 90555 159990 152562 78345 20325 2295 85 polytope > print \$p->VERTICES; 1 1 5 3 1 6 2 5 5 3 1 3 5 6 1 1 1 1 4 2 6 3 3 5 1 6 2 6 1 2 5 1 1 1 2 4 6 3 5 3 1 6 2 2 5 6 1 1 1 1 2 1 6 6 5 6 1 3 5 2 2 3 1 4 1 1 5 1 3 6 2 5 5 3 3 1 5 6 1 1 1 1 4 6 2 3 3 1 5 6 6 2 1 2 1 5 1 1 2 6 1 6 5 1 6 3 2 5 2 3 4 1 1 1 2 6 4 3 5 1 3 6 2 2 5 6 1 1 1 1 5 5 2 3 3 1 5 6 6 1 1 3 1 5 1 1 6 5 1 3 1 2 6 6 5 3 1 2 2 4 1 1 2 5 5 3 5 1 3 6 3 1 5 6 1 1 1 1 6 2 4 3 1 5 3 6 2 6 1 2 5 1 1 1 5 1 3 6 2 6 4 3 2 2 5 6 1 1 1 1 5 2 5 3 1 5 3 6 3 6 1 1 5 1 1 1 2 5 5 3 5 3 1 6 1 3 5 6 1 1 1 1 6 4 2 3 1 3 5 6 6 2 1 2 1 5 1 1 5 2 5 3 3 5 1 6 1 6 1 3 5 1 1 1 3 5 1 6 5 2 5 3 1 6 1 3 5 1 1 1 6 2 1 6 1 5 6 3 2 3 4 5 2 1 1 1 5 6 1 3 2 1 6 6 5 2 2 3 1 4 1 1 5 1 6 3 2 6 1 6 2 5 2 3 4 1 1 1 1 2 6 6 6 5 1 3 5 3 1 2 2 4 1 1 1 5 6 3 6 2 1 6 2 3 4 5 2 1 1 1 1 6 2 6 6 1 5 3 3 5 1 2 4 2 1 1 3 1 5 6 5 5 2 3 6 1 1 3 1 5 1 1 6 1 2 6 1 6 5 3 3 2 4 5 1 2 1 1 1 3 5 6 6 4 2 3 6 2 1 2 1 5 1 1 1 3 5 6 5 5 2 3 6 3 1 1 1 5 1 1 1 5 3 6 5 2 5 3 3 6 1 1 5 1 1 1 5 3 1 6 2 4 6 3 2 2 5 6 1 1 1 1 6 1 5 3 1 6 2 6 3 5 1 2 4 2 1 1 1 5 3 6 6 2 4 3 2 6 1 2 5 1 1 1 3 5 1 6 4 2 6 3 2 6 1 2 5 1 1 1 3 1 5 6 4 6 2 3 6 2 1 2 1 5 1 1 5 5 2 3 1 3 5 6 6 3 1 1 1 5 1 1 1 6 5 3 6 1 2 6 3 2 4 5 1 2 1 1 2 4 4 5 1 5 5 4 4 4 5 2 1 1 1 1 3 2 6 4 6 5 1 3 5 1 1 2 2 6 1 1 3 6 2 4 6 1 5 3 1 5 1 2 6 2 1 1 1 5 5 4 2 4 4 5 4 4 5 2 1 1 1 1 6 3 1 5 1 6 6 2 1 3 5 4 2 2 1 1 1 5 4 5 2 4 5 4 4 5 4 1 2 1 1 1 1 6 6 2 6 3 1 5 1 3 5 4 2 2 1 1 1 4 5 5 2 5 4 4 5 4 4 1 1 2 1 1 6 3 1 5 3 5 5 2 1 1 5 6 1 3 1 1 2 4 5 4 1 5 4 5 4 5 4 1 2 1 1 1 3 4 6 2 6 3 1 5 1 1 5 6 2 2 1 1 2 5 4 4 1 4 5 5 5 4 4 1 1 2 1 1 6 6 2 1 1 3 5 6 4 2 3 2 1 5 1 1 3 5 1 6 6 2 6 1 2 4 1 2 5 3 1 1 6 3 1 5 3 4 6 2 1 1 5 6 2 2 1 1 6 1 3 5 3 5 6 1 1 1 5 5 4 1 1 1 3 1 6 5 6 6 1 2 4 1 2 3 2 5 1 1 6 6 1 2 3 1 6 5 4 1 2 3 2 5 1 1 6 1 6 2 3 6 1 5 1 4 2 3 5 2 1 1 6 2 6 1 3 5 1 6 2 4 1 2 5 3 1 1 1 6 3 5 5 3 5 2 1 6 3 1 5 1 1 1 6 1 3 5 3 5 5 2 1 1 5 6 3 1 1 1 2 2 4 7 4 4 5 2 8 1 1 1 1 5 1 1 4 2 4 5 5 1 5 4 4 2 1 4 5 1 1 1 2 1 5 7 4 5 4 2 7 2 1 1 2 4 1 1 2 1 5 7 5 4 4 2 7 1 1 2 2 4 1 1 5 4 1 5 1 2 8 4 7 1 2 2 1 4 1 1 1 8 2 4 8 1 4 2 1 4 2 2 4 4 1 1 2 4 7 2 5 1 2 7 4 1 4 5 2 1 1 1 4 4 5 2 2 2 4 7 8 1 1 1 1 5 1 1 3 2 5 5 6 5 3 1 5 1 1 1 3 6 1 1 4 1 5 5 5 2 4 4 5 1 1 4 4 2 1 1 5 1 4 5 4 2 5 4 4 1 2 5 4 1 1 1 4 2 7 2 2 4 2 7 4 5 1 1 5 1 1 1 2 4 2 7 4 2 7 2 4 5 1 1 5 1 1 1 4 5 2 4 1 2 7 5 7 2 2 1 1 4 1 1 2 5 7 1 4 1 2 8 5 1 4 4 1 2 1 1 4 1 8 2 2 5 1 7 5 4 1 1 4 2 1 1 4 4 2 5 2 2 7 4 8 1 1 1 1 5 1 1 1 2 4 8 5 4 5 1 7 2 1 1 2 4 1 1 4 2 7 2 1 5 2 7 4 5 2 1 4 1 1 1 2 4 8 1 4 2 1 8 4 2 4 4 2 1 1 1 1 5 2 7 4 2 7 2 4 5 2 1 4 1 1 1 5 4 4 2 2 1 5 7 7 1 1 2 2 4 1 1 4 2 8 1 2 4 1 8 4 4 2 2 4 1 1 1 4 2 5 4 5 1 4 5 4 1 2 5 4 1 1 1 1 4 2 8 5 2 7 1 5 4 1 1 4 2 1 1 2 4 7 2 4 2 2 7 4 1 5 5 1 1 1 1 5 4 5 1 1 2 4 8 7 2 1 1 2 4 1 1 5 1 7 2 2 4 2 7 4 4 1 2 5 1 1 1 2 1 4 8 4 5 5 1 7 1 2 2 1 4 1 1 4 1 2 8 2 5 7 1 5 1 4 4 1 2 1 1 5 2 7 1 1 4 2 8 5 4 1 1 4 2 1 1 1 5 5 4 5 1 4 5 4 1 5 5 1 1 1 1 5 1 2 7 2 4 7 2 4 1 4 5 2 1 1 1 1 5 2 7 5 1 7 2 4 4 2 2 4 1 1 1 4 5 5 1 2 1 4 8 7 1 2 2 1 4 1 1 5 1 5 4 1 5 4 5 4 5 1 1 5 1 1 1 4 5 1 5 2 1 8 4 7 2 1 1 2 4 1 1 1 2 8 4 5 4 1 5 7 1 2 2 1 4 1 1 5 4 2 4 2 1 7 5 7 1 1 2 2 4 1 1 1 5 7 2 4 2 2 7 4 2 5 4 1 1 1 1 5 2 1 7 1 4 8 2 5 1 4 4 1 2 1 1 2 5 1 7 4 1 8 2 5 4 1 1 4 2 1 1 5 1 3 6 1 5 6 3 4 1 5 5 1 1 1 1 5 1 2 7 1 5 7 2 4 2 4 4 2 1 1 1 1 2 5 7 5 4 4 2 7 1 2 2 1 4 1 1 5 4 2 4 1 2 7 5 7 2 1 1 2 4 1 1 1 2 7 5 4 5 2 4 7 2 2 1 1 4 1 1 1 2 7 5 5 4 2 4 7 2 1 1 2 4 1 1 5 1 6 3 1 5 3 6 4 5 1 1 5 1 1 1 1 5 6 3 5 1 3 6 4 1 5 5 1 1 1 1 4 5 2 4 2 1 7 5 7 1 2 2 1 4 1 1 2 1 8 4 4 5 1 5 7 2 1 1 2 4 1 1 4 5 4 2 2 1 5 7 7 2 1 1 2 4 1 1 1 2 5 7 4 5 4 2 7 2 2 1 1 4 1 1 1 5 7 2 5 1 2 7 4 2 4 4 2 1 1 1 2 1 7 5 4 5 2 4 7 1 2 2 1 4 1 1 2 1 7 5 5 4 2 4 7 1 1 2 2 4 1 1 1 8 4 2 8 1 2 4 1 2 4 4 2 4 1 1 4 5 4 2 1 2 5 7 7 2 2 1 1 4 1 1 5 1 5 4 4 2 4 5 4 2 1 4 5 1 1 1 1 5 4 5 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1 1 5 1 4 1 1 1 4 5 5 5 1 2 2 4 7 1 4 4 1 5 2 1 7 5 1 2 1 8 4/3 4/3 4/3 4 4/3 4/3 4/3 4 8 4 4/3 4 4/3 16/3 1 5 4 4 2 1 1 1 5 4 8 1 2 1 2 7 1 2 7 1 1 5 1 7 4 2 2 2 4 5 1 4 1 2 1 4 5 4 1 4 5 4 5 4 5 1 2 1 1 4 1 1 5 5 5 5 1 1 5 4 1 1 4 5 1 6 3 1 1 5 1 3 1 5 6 5 1 5 1 4 1 2 2 1 7 4 5 7 1 1 4 1 4 2 2 5 1 2 5 4 4 1 2 4 1 7 1 7 1 2 5 2 1 3 5 6 1 1 2 1 5 5 5 3 1 1 3 6 1 2 1 4 4 5 7 4 1 2 5 2 1 2 1 7 1 6 5 1 1 3 5 3 1 1 2 2 2 6 4 6 1 2 1 5 7 1 7 1 1 5 2 2 4 4 4 2 1 6 2 6 1 1 2 4 1 3 2 5 5 3 1 6 1 5 5 1 2 3 6 1 3 1 3 1 1 5 6 5 1 2 4 5 4 1 4 5 4 1 1 2 5 1 4 5 1 7 1 2 1 5 2 1 2 4 7 5 1 4 2 4 1 4 8 4/3 4/3 4/3 4 4/3 4/3 16/3 4/3 4/3 4/3 8 4 4 1 4 1 2 4 5 5 4 2 1 7 1 2 2 1 7 1 2 7 1 5 1 1 7 2 4 2 4 2 1 5 4 1 4 2 5 4 1 2 7 2 1 1 4 7 1 2 5 1 4 7 2 2 1 5 2 4 1 1 1 2 4 7 5 1 5 5 3 2 1 6 1 3 1 1 1 3 5 6 5 1 3 5 1 6 1 2 4 1 6 2 5 2 3 6 1 1 2 7 5 1 1 1 2 7 4 4 2 2 1 4 5 1 2 1 4 7 2 4 1 1 8 5 2 4 5 1 1 1 7 1 1 5 2 2 2 4 1 5 4 4 1 7 2 1 16/3 4/3 4 4 4/3 4 4/3 4/3 4 4/3 4/3 8 8 4/3 4/3 1 2 1 1 8 4 4 4 2 4 8 1 2 1 2 4 1 5 1 4 2 4 4 1 5 1 2 7 2 1 8 1 1 4 1 2 8 1 5 1 4 2 4 1 5 2 7 1 1 4 2 5 4 1 4 1 2 5 2 1 7 7 1 2 1 2 5 1 1 7 5 4 4 1 1 1 4 8 2 2 1 2 3 5 5 1 5 3 1 5 1 1 6 6 1 3 1 2 4 5 1 4 4 1 7 2 1 5 2 2 7 1 1 2 4 1 5 4 4 1 5 4 5 1 2 4 5 1 1 3 1 1 6 5 6 4 1 2 6 1 2 3 2 5 1 8 2 4 1 1 2 4 1 1 4 4 4 2 2 8 1 7 1 2 2 4 2 1 1 5 7 4 2 5 1 4 1 5 3 6 1 1 2 5 1 3 1 5 5 3 1 6 1 4 2 4 5 1 4 2 1 5 2 1 7 7 1 2 1 4 4 2 1 5 2 4 5 1 2 1 7 7 1 2 1 2 1 2 7 4 5 4 1 4 7 2 1 1 2 5 1 5 1 1 4 5 1 3 1 6 6 5 3 5 1 1 1 3 1 1 6 5 6 5 1 1 5 3 1 1 4 5 1 3 6 1 1 5 1 6 5 1 3 1 5 5 1 4 1 4 2 7 2 1 2 5 4 1 1 4 7 1 2 5 1 7 1 1 2 5 2 2 1 4 8 4 1 4 1 5 1 7 2 1 5 1 1 2 4 2 7 2 4 1 5 4 1 4/3 8 4/3 4/3 4 4/3 8 4 4/3 4/3 4/3 4 4 4/3 16/3 1 2 4 5 4 1 4 2 1 7 1 2 5 7 1 2 1 5 4 1 5 1 1 1 6 3 5 1 5 3 6 1 1 6 5 1 1 3 5 1 3 1 4 1 1 5 5 6 1 4 4 5 2 1 2 7 1 2 1 4 5 2 1 7 1 4 4/3 16/3 4 4/3 4/3 4/3 8 4/3 4 4/3 8 4/3 4 4/3 1 4 4 2 2 4 2 1 1 8 4 4 2 8 1 1 1 2 1 7 2 4 7 1 4 2 2 5 1 1 5 4 1 5 4 4 1 2 1 1 4 5 8 2 1 2 1 7 1 5 3 1 6 1 1 4 5 1 5 1 6 1 5 3 1 3 6 5 1 1 1 2 4 6 5 3 1 2 2 6 1 4 6 1 3 2 6 3 1 2 1 1 2 6 5 5 1 2 6 1 1 6 2 5 5 2 3 1 4 6 1 3 1 3 5 1 1 6 2 6 4 1 2 2 5 6 1 3 1 5 3 6 1 1 2 5 2 2 1 6 4 1 3 6 1 3 1 5 6 1 5 1 1 6 2 3 5 5 3 1 1 2 4 1 4 5 4 1 4 5 5 2 1 5 4 1 1 5 3 1 6 1 2 2 5 2 4 1 6 3 6 1 1 2 6 1 3 4 2 5 5 2 1 1 6 6 3 1 1 3 1 4 6 2 6 1 1 5 3 1 5 6 2 2 1 4 2 5 4 1 4 1 2 5 5 4 1 1 4 5 1 2 4 4 4 2 1 4 1 8 2 8 1 2 4 1 1 2 4 8 1 1 1 2 7 4 4 2 5 1 1 5 1 4 4 2 5 1 2 2 7 1 4 1 5 1 7 2 1 2 2 1 7 4 4 5 1 4 7 1 2 2 1 5 1 3 1 5 2 5 6 1 5 1 3 5 1 1 6 3 1 3 2 5 5 1 5 1 1 6 1 3 5 6 3 1 1 8 2 1 1 4 2 1 1 4 7 4 1 5 2 5 1 8 2 1 1 4 2 1 1 4 4 4 4 8 2 2 1 3 6 1 1 5 1 5 6 1 3 1 5 5 2 3 1 2 1 7 5 1 4 1 2 7 2 4 5 4 2 1 1 5 1 6 3 1 2 5 2 2 3 4 6 1 1 6 1 1 5 6 1 3 1 3 6 5 5 3 2 1 1 5 1 1 1 6 3 5 6 1 5 3 3 5 1 1 5 2 1 1 1 5 6 3 5 3 1 6 2 3 5 5 1 1 1 1 6 1 5 3 3 6 1 5 1 5 1 3 5 2 1 1 1 5 6 3 6 1 3 5 3 1 5 5 2 1 1 1 3 6 5 1 5 1 3 6 1 2 5 5 3 1 1 1 5 1 6 3 3 6 1 5 1 5 2 3 5 1 1 1 5 3 6 1 3 5 1 6 2 5 1 1 5 3 1 1 1 6 3 5 6 3 5 1 1 5 3 1 5 2 1 1 3 1 6 5 5 6 1 3 5 1 2 3 1 5 1 1 3 5 6 1 5 1 3 6 2 1 5 5 3 1 1 1 6 1 5 3 1 6 3 5 3 5 1 1 5 2 1 1 6 3 5 1 3 5 1 6 1 5 1 2 5 3 1 1 6 5 3 1 3 1 5 6 5 1 1 2 3 5 1 1 6 1 3 5 3 6 5 1 1 1 5 5 3 2 1 1 1 5 6 3 6 3 1 5 1 3 5 5 2 1 1 1 1 6 5 3 6 1 3 5 3 1 5 5 1 2 1 1 5 6 3 1 1 3 5 6 5 2 3 1 1 5 1 1 6 5 1 3 1 3 6 5 5 3 1 1 2 5 1 1 1 3 6 5 6 5 1 3 5 3 1 1 2 5 1 1 5 1 6 3 3 5 1 6 2 5 1 3 5 1 1 1 3 6 5 1 5 3 1 6 1 2 5 5 1 3 1 1 1 6 5 3 5 1 3 6 3 2 5 5 1 1 1 1 6 3 1 5 1 5 6 3 1 3 5 5 2 1 1 1 6 5 1 3 3 1 6 5 5 1 1 3 2 5 1 1 3 5 6 1 5 3 1 6 2 1 5 5 1 3 1 1 1 6 5 3 6 3 1 5 1 3 5 5 1 2 1 1 5 1 6 3 1 6 3 5 3 5 2 1 5 1 1 1 6 1 3 5 1 6 5 3 3 1 5 5 1 2 1 1 1 3 6 5 6 5 3 1 5 1 3 1 2 5 1 1 3 6 1 5 6 1 5 3 1 5 1 3 5 2 1 1 3 1 5 6 5 6 3 1 5 2 1 1 3 5 1 1 1 3 5 6 6 5 3 1 5 1 3 2 1 5 1 1 6 3 5 1 1 6 3 5 1 5 3 1 5 2 1 1 3 6 5 1 6 1 3 5 1 1 5 5 3 2 1 1 3 6 1 5 5 3 6 1 1 5 2 1 5 3 1 1 1 6 3 5 5 1 6 3 3 5 2 1 5 1 1 1 3 1 5 6 6 5 3 1 5 1 1 2 3 5 1 1 6 5 3 1 1 3 6 5 5 1 3 1 2 5 1 1 1 5 3 6 6 3 5 1 1 5 3 2 5 1 1 1 5 3 1 6 3 5 6 1 2 1 5 5 1 3 1 1 6 1 3 5 1 5 6 3 3 1 5 5 2 1 1 1 5 1 3 6 3 6 5 1 1 2 5 5 3 1 1 1 6 3 1 5 1 6 5 3 1 3 5 5 1 2 1 1 3 5 1 6 5 1 6 3 2 5 1 3 5 1 1 1 5 1 3 6 1 6 5 3 3 2 5 5 1 1 1 1 6 3 1 5 3 5 6 1 1 1 5 5 2 3 1 1 6 1 5 3 1 5 3 6 3 5 1 2 5 1 1 1 5 3 1 6 3 6 5 1 1 2 5 5 1 3 1 1 5 6 1 3 3 1 6 5 5 1 2 3 1 5 1 1 1 5 3 6 5 3 6 1 2 5 3 1 5 1 1 1 1 5 3 6 6 1 5 3 3 5 1 2 5 1 1 1 5 3 1 6 1 5 6 3 2 3 5 5 1 1 1 1 3 1 6 5 6 5 1 3 5 1 1 3 2 5 1 1 6 5 3 1 1 3 5 6 5 1 3 2 1 5 1 1 1 3 5 6 6 5 1 3 5 3 1 2 1 5 1 1 6 3 5 1 1 5 3 6 1 5 3 2 5 1 1 1 5 6 3 1 3 1 5 6 5 2 1 1 3 5 1 1 3 6 1 5 5 1 6 3 1 5 2 3 5 1 1 1 5 6 3 1 3 1 6 5 5 1 2 1 3 5 1 1 5 6 1 3 3 1 5 6 5 2 1 3 1 5 1 1 6 5 1 3 1 3 5 6 5 3 1 2 1 5 1 1 3 1 6 5 5 6 3 1 5 1 2 1 3 5 1 1 1 3 6 5 5 6 1 3 5 3 2 1 1 5 1 1 3 5 6 1 6 3 1 5 1 1 5 5 2 3 1 1 5 1 3 6 3 5 6 1 2 1 5 5 3 1 1 1 5 3 6 1 3 6 1 5 1 5 2 1 5 3 1 1 3 5 1 6 6 3 5 1 1 5 1 2 5 3 1 1 3 1 5 6 5 6 1 3 5 2 1 3 1 5 1 1 5 3 6 1 1 5 3 6 2 5 3 1 5 1 1 1 3 5 1 6 5 3 6 1 2 5 1 1 5 3 1 1 1 3 5 6 5 6 3 1 5 2 3 1 1 5 ----------------- alternate n=6 ----------------- polytope > \$inequalities=new Matrix ([[-16,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0],[-16,1,0,0,0,0,1,1,1,1,0,0,0,0,0,0],[-16,0,1,0,0,0,1,0,0,0,1,1,1,0,0,0],[-16,0,0,1,0,0,0,1,0,0,1,0,0,1,1,0],[-16,0,0,0,1,0,0,0,1,0,0,1,0,1,0,1],[-16,0,0,0,0,1,0,0,0,1,0,0,1,0,1,1],[16,-1,-1,-1,-1,-1,0,0,0,0,0,0,0,0,0,0],[16,-1,0,0,0,0,-1,-1,-1,-1,0,0,0,0,0,0],[16,0,-1,0,0,0,-1,0,0,0,-1,-1,-1,0,0,0],[16,0,0,-1,0,0,0,-1,0,0,-1,0,0,-1,-1,0],[16,0,0,0,-1,0,0,0,-1,0,0,-1,0,-1,0,-1],[16,0,0,0,0,-1,0,0,0,-1,0,0,-1,0,-1,-1],[-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[-1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0],[-1,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0],[-1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0],[-1,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0],[-1,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0],[-1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0],[-1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0],[-1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0],[-1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0],[-1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0],[-1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0],[-1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0],[-1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0],[-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1],[16,-1,-1,0,0,0,-1,0,0,0,0,0,0,0,0,0],[16,-1,0,-1,0,0,0,-1,0,0,0,0,0,0,0,0],[16,-1,0,0,-1,0,0,0,-1,0,0,0,0,0,0,0],[16,-1,0,0,0,-1,0,0,0,-1,0,0,0,0,0,0],[16,0,-1,-1,0,0,0,0,0,0,-1,0,0,0,0,0],[16,0,-1,0,-1,0,0,0,0,0,0,-1,0,0,0,0],[16,0,-1,0,0,-1,0,0,0,0,0,0,-1,0,0,0],[16,0,0,-1,-1,0,0,0,0,0,0,0,0,-1,0,0],[16,0,0,-1,0,-1,0,0,0,0,0,0,0,0,-1,0],[16,-1,-1,0,0,0,-1,0,0,0,0,0,0,0,0,0],[16,-1,0,-1,0,0,0,-1,0,0,0,0,0,0,0,0],[16,0,-1,-1,0,0,0,0,0,0,-1,0,0,0,0,0],[16,-1,0,0,-1,0,0,0,-1,0,0,0,0,0,0,0],[16,0,-1,0,-1,0,0,0,0,0,0,-1,0,0,0,0],[16,0,0,-1,-1,0,0,0,0,0,0,0,0,-1,0,0],[16,0,0,0,-1,-1,0,0,0,0,0,0,0,0,0,-1],[16,-1,0,0,0,-1,0,0,0,-1,0,0,0,0,0,0],[16,0,-1,0,0,-1,0,0,0,0,0,0,-1,0,0,0],[16,0,0,-1,0,-1,0,0,0,0,0,0,0,0,-1,0],[16,0,0,0,-1,-1,0,0,0,0,0,0,0,0,0,-1],[8,1,-1,0,0,0,-1,0,0,0,0,0,0,0,0,0],[8,1,0,-1,0,0,0,-1,0,0,0,0,0,0,0,0],[8,1,0,0,-1,0,0,0,-1,0,0,0,0,0,0,0],[8,1,0,0,0,-1,0,0,0,-1,0,0,0,0,0,0],[8,-1,1,0,0,0,-1,0,0,0,0,0, 0,0,0,0],[8,0,1,-1,0,0,0,0,0,0,-1,0,0,0,0,0],[8,0,1,0,-1,0,0,0,0,0,0,-1,0,0,0,0],[8,0,1,0,0,-1,0,0,0,0,0,0,-1,0,0,0],[8,-1,0,1,0,0,0,-1,0,0,0,0,0,0,0,0],[8,0,-1,1,0,0,0,0,0,0,-1,0,0,0,0,0],[8,0,0,1,-1,0,0,0,0,0,0,0,0,-1,0,0],[8,0,0,1,0,-1,0,0,0,0,0,0,0,0,-1,0],[8,-1,0,0,1,0,0,0,-1,0,0,0,0,0,0,0],[8,0,-1,0,1,0,0,0,0,0,0,-1,0,0,0,0],[8,0,0,-1,1,0,0,0,0,0,0,0,0,-1,0,0],[8,0,0,0,1,-1,0,0,0,0,0,0,0,0,0,-1],[8,-1,0,0,0,1,0,0,0,-1,0,0,0,0,0,0],[8,0,-1,0,0,1,0,0,0,0,0,0,-1,0,0,0],[8,0,0,-1,0,1,0,0,0,0,0,0,0,0,-1,0],[8,0,0,0,-1,1,0,0,0,0,0,0,0,0,0,-1],[8,-1,-1,0,0,0,1,0,0,0,0,0,0,0,0,0],[8,0,0,0,0,0,1,-1,0,0,-1,0,0,0,0,0],[8,0,0,0,0,0,1,0,-1,0,0,-1,0,0,0,0],[8,0,0,0,0,0,1,0,0,-1,0,0,-1,0,0,0],[8,-1,0,-1,0,0,0,1,0,0,0,0,0,0,0,0],[8,0,0,0,0,0,-1,1,0,0,-1,0,0,0,0,0],[8,0,0,0,0,0,0,1,-1,0,0,0,0,-1,0,0],[8,0,0,0,0,0,0,1,0,-1,0,0,0,0,-1,0],[8,-1,0,0,-1,0,0,0,1,0,0,0,0,0,0,0],[8,0,0,0,0,0,-1,0,1,0,0,-1,0,0,0,0],[8,0,0,0,0,0,0,-1,1,0,0,0,0,-1,0,0],[8,0,0,0,0,0,0,0,1,-1,0,0,0,0,0,-1],[8,-1,0,0,0,-1,0,0,0,1,0,0,0,0,0,0],[8,0,0,0,0,0,-1,0,0,1,0,0,-1,0,0,0],[8,0,0,0,0,0,0,-1,0,1,0,0,0,0,-1,0],[8,0,0,0,0,0,0,0,-1,1,0,0,0,0,0,-1],[8,0,0,0,0,0,-1,-1,0,0,1,0,0,0,0,0],[8,0,0,0,0,0,0,0,0,0,1,-1,0,-1,0,0],[8,0,0,0,0,0,0,0,0,0,1,0,-1,0,-1,0],[8,0,-1,0,-1,0,0,0,0,0,0,1,0,0,0,0],[8,0,0,0,0,0,-1,0,-1,0,0,1,0,0,0,0],[8,0,0,0,0,0,0,0,0,0,-1,1,0,-1,0,0],[8,0,0,0,0,0,0,0,0,0,0,1,-1,0,0,-1],[8,0,-1,0,0,-1,0,0,0,0,0,0,1,0,0,0],[8,0,0,0,0,0,-1,0,0,-1,0,0,1,0,0,0],[8,0,0,0,0,0,0,0,0,0,-1,0,1,0,-1,0],[8,0,0,0,0,0,0,0,0,0,0,-1,1,0,0,-1],[8,0,0,-1,-1,0,0,0,0,0,0,0,0,1,0,0],[8,0,0,0,0,0,0,-1,-1,0,0,0,0,1,0,0],[8,0,0,0,0,0,0,0,0,0,-1,-1,0,1,0,0],[8,0,0,0,0,0,0,0,0,0,0,0,0,1,-1,-1],[8,0,0,-1,0,-1,0,0,0,0,0,0,0,0,1,0],[8,0,0,0,0,0,0,-1,0,-1,0,0,0,0,1,0],[8,0,0,0,0,0,0,0,0,0,-1,0,-1,0,1,0],[8,0,0,0,0,0,0,0,0,0,0,0,0,-1,1,-1],[8,0,0,0,-1,-1,0,0,0,0,0,0,0,0,0,1],[8,0,0,0,0,0,0,0,-1,-1,0,0,0,0,0,1],[8,0,0,0,0,0,0,0,0,0,0,-1,-1,0,0,1],[8,0,-1,-1,0,0,0,0,0,0,1,0,0,0,0,0],[8,0,0,0,0,0,0,0,0,0,0,0,0,-1,-1,1]]); polytope > \$p=new Polytope(INEQUALITIES=>\$inequalities); polytope > print \$p->F_VECTOR;