Differences
This shows you the differences between two versions of the page.
Both sides previous revision Previous revision Next revision | Previous revision | ||
tutorial:face_lattice_tutorial [2011/11/07 18:26] – joswig | user_guide:tutorials:face_lattice_tutorial [2019/02/04 22:55] (current) – external edit 127.0.0.1 | ||
---|---|---|---|
Line 1: | Line 1: | ||
- | ====== Face lattices (of Polytopes) ====== | + | {{page> |
- | By definition the face lattice of a polytope contains all the combinatorial information about a polytope. | ||
- | |||
- | < | ||
- | polytope > $p = n_gon(5); | ||
- | polytope > $HD = $p-> | ||
- | polytope > print $HD-> | ||
- | {} | ||
- | {0} | ||
- | {1} | ||
- | {2} | ||
- | {3} | ||
- | {4} | ||
- | {1 2} | ||
- | {2 3} | ||
- | {3 4} | ||
- | {0 4} | ||
- | {0 1} | ||
- | {0 1 2 3 4} | ||
- | </ | ||
- | |||
- | The obvious question is: How to interpret that output? | ||
- | |||
- | Very often just a part of the face lattice is interesting. | ||
- | < | ||
- | polytope > for (my $k=$HD-> | ||
- | {1 2}{2 3}{3 4}{0 4}{0 1} | ||
- | </ | ||
- | The above works as described since DIMS return an array with the first nodes of each dimension. | ||
- | |||
- | Face lattices of polytopes can be huge. So it may be an advantage to compute only a part. The following computes the 2-skeleton of an 8-dimensional cube. | ||
- | < | ||
- | polytope > $c=cube(8); | ||
- | polytope > $HD_partial = hasse_diagram($c-> | ||
- | polytope > print $HD_partial-> | ||
- | 1 257 1281 3073 | ||
- | </ | ||
- | Instead of listing all those thousands of faces here we give only the vector of starting nodes. |