I'd like to do computations with incidence matrices of abstract polytopes. There's a database mentioned in this older post :

what abstract regular polyhedra exist?

but I don't see extract the incidence matrices from what's provided. I can find vertix-edge graphs for a number of cases, but I need the full relations (vertix-edge, edge-face,...). Are there any software packages (for GAP, Sage, ...) that have such a database and some utilities to work with it? Even a small set of familiar examples (paltonic solids,...) would be good to start with.

  • 1
    $\begingroup$ Have you looked at polymake (which has a GAP interface), and its associated database? $\endgroup$
    – ahulpke
    Aug 9, 2020 at 21:53
  • $\begingroup$ I'll give that a try. It might be overkill for what I'm looking for. It's just the incidence matrices that I'm after; the geometric data is not necessary....Thanks for the suggestion. $\endgroup$
    – unknown
    Aug 9, 2020 at 23:49
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    $\begingroup$ In addition: The Atlas of Small Regular Polytopes by Michael Hartley, and An Atlas of Polytopes for Small Almost Simple Groups by Laurence Vauthier and Dimitri Leemans. $\endgroup$ Aug 10, 2020 at 10:44

1 Answer 1


The incidence matrices in its generality, i.e. way beyond the regular solids only, is essentially my own elaboration. You might be welcome to look into my website at https://bendwavy.org/klitzing/home.htm which provides to my knowledge the most encompassing list of elaborated incidence matrices, even if all those have been worked out manually in the sequel of half a lifetime.

--- rk


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