------------------------------------ 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) I put the initial “1” in each point. ------------------------------------ INPUT/OUTPUT ------------------------------------ polytope > \$points=new Matrix([[1,3, 3, 2, 1], [1, 3, 3, 1, 2], [1, 3, 2, 3, 1], [1, 3, 2, 1, 3], [1, 3, 1, 3, 2], [1, 3, 1, 2, 3], [1, 2, 3, 3, 1], [1, 2, 3, 1, 3], [1, 2, 1, 3, 3], [1, 1, 3, 3, 2],[1, 1, 3, 2, 3], [1, 1, 2, 3, 3],[1,2,2,2,2]]); polytope > \$p=new Polytope(POINTS=>\$points); polytope > print \$p->F_VECTOR; 13 30 26 9 polytope > print \$p->VERTICES_IN_FACETS; {0 1 2 3 4 5 6 7 8 9 10 11} {0 1 2 3 4 5 12} {0 1 6 7 9 10 12} {2 4 6 8 9 11 12} {9 10 11 12} {3 5 7 8 10 11 12} {4 5 8 12} {1 3 7 12} {0 2 6 12}