Ask Your Question

Hasse diagram of different dimensional cells of a polyhedron

asked 2021-10-10 09:01:44 +0200

arboreal_vf gravatar image

updated 2021-10-10 12:58:58 +0200

slelievre gravatar image

I am trying to get a facet poset diagram of a polyhedron. What I want is an adjacency matrix describing the Hasse diagram/poset where vertices are cells, and two vertices are connected by an edge if one of their corresponding cells is contained in the other.

So I want a Hasse diagram where the top row consists of a vertex for the highest dimensional cell, then the next row consists of cells of one less dimension, and so on until the final row corresponding to vertices.

For instance, I have:

E = polytopes.dodecahedron().face_lattice()

I don't know how to extract this kind of information from this.

I want to be able to plot the cell poset diagram in some other software to look at it.

edit retag flag offensive close merge delete


Not clear to me what more you would like to have. E is exactly what you want, except for the added empty face of dimension -1. You can see the Hasse diagram using E.plot(label_elements=False).

FrédéricC gravatar imageFrédéricC ( 2021-10-10 14:15:28 +0200 )edit

1 Answer

Sort by » oldest newest most voted

answered 2021-10-10 20:10:22 +0200

FrédéricC gravatar image

To get a matrix, you can do

sage: L = polytopes.dodecahedron().face_lattice()
sage: L.hasse_diagram().adjacency_matrix()
64 x 64 dense matrix over Integer Ring (use the '.str()' method to see the entries)

and if you want to get rid of the empty face before, you can use

sage: L = L.subposet([f for f in L if f.dimension()>=0])
edit flag offensive delete link more

Your Answer

Please start posting anonymously - your entry will be published after you log in or create a new account.

Add Answer

Question Tools


Asked: 2021-10-10 09:01:44 +0200

Seen: 156 times

Last updated: Oct 10 '21