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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.

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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

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

Seen: 45 times

Last updated: Oct 10