Exporting incidence relations

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nikobreu
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Exporting incidence relations

Post by nikobreu » Tue Mar 10, 2020 1:04 pm

Is there a way to export the incidence relation between the faces <-> edges and edges <-> vertices of a given polytope in Stella? Alternatively, is there some export option that would it make easy to retrieve this information?

What I had in mind was e.g. for the relations faces <-> edges of the cube I would like to have a 6x12 binary matrix A such that A_ij = 1 iff face i is bounded by edge j and A_ij = 0 otherwise.

Sorry if this was asked before, but searching for "incidence" did not bring up any results.

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robertw
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Re: Exporting incidence relations

Post by robertw » Wed Mar 11, 2020 1:48 am

There's no incidence matrix as such. And you can't export 4D polytopes as 4D data. But for 3D polyhedra you can export to .OFF format, which gives a list of vertices, and then a list of vertex indices for each face. You may be able to extract what you need from that.

And just curious, but what do you need the incidence matrix for? How can it be used?

nikobreu
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Re: Exporting incidence relations

Post by nikobreu » Wed Mar 11, 2020 11:27 am

Dear Robert,

Thank you for the quick reply. Okay, I will try the OFF export.

Is there a way of doing this for several polytopes at once? The reason for doing this is to do some automated search for polytopes with a given ratio of vertices and faces, as well as a 3-coloring of vertices.

The incidence matrix of a polytope can be useful for constructing "quantum error correcting codes" which enable us to protect fragile quantum states against noise/errors. The rough idea is that vertices, edges and faces correspond to degrees of freedom (qubits) and quantum mechanical observables. The incidence relation defines to which degrees of freedom the observables have access.
For example, the dodecadodecahedron turns out to directly define a pretty nice quantum code, see page 4 of https://arxiv.org/pdf/1703.00590.pdf.

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robertw
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Re: Exporting incidence relations

Post by robertw » Thu Mar 12, 2020 2:02 am

Sorry there's no way to batch export. But hopefully the .OFF format contains what you need.

nikobreu
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Re: Exporting incidence relations

Post by nikobreu » Thu Mar 12, 2020 12:19 pm

Okay, thanks a lot for the quick help again!

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