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added remark for plantri
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Moritz Firsching
Moritz Firsching
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You can find Frank Lutz's lists of simplicial spheres (and other manifolds) here:

Let me shamelessly self-advertise my list of simplicial 4-polytopes with up to $10$ vertices and various families of neighborly polytopes here. I give realization with rational coordinates (inscribed, if possible). You can extract the lists of facets easily from the coordinates. For the simplicial 4-polytopes with 10 vertices I use the same numbering as Frank Lutz uses for the simplicial 3-spheres. Of course some of the spheres are non-realizable ($85\ 878$ to be precise), and then the corresponding number does not appear in my list.

There is an arxiv preprint summarizing the results: Realizability and inscribability for some simplicial spheres and matroid polytopes.

You might also be interested in the following pages by Hiroyuki Miyata:

and Lukas Finschi's "Homepage of Oriented Matroids".

For (simplicial) 3-dimensional polytopes, it is very very fast to generate the combinatorial types of triangulations using plantri, by Gunnar Brinkmann and Brendan McKay, so there really is no need for a database. (At least for polytopes with a small number of vertices. A database of "interesting polytopes" and not "all polytopes up to a certian number of vertices" would still be something nice to have)

You can find Frank Lutz's lists of simplicial spheres (and other manifolds) here:

Let me shamelessly self-advertise my list of simplicial 4-polytopes with up to $10$ vertices and various families of neighborly polytopes here. I give realization with rational coordinates (inscribed, if possible). You can extract the lists of facets easily from the coordinates. For the simplicial 4-polytopes with 10 vertices I use the same numbering as Frank Lutz uses for the simplicial 3-spheres. Of course some of the spheres are non-realizable ($85\ 878$ to be precise), and then the corresponding number does not appear in my list.

There is an arxiv preprint summarizing the results: Realizability and inscribability for some simplicial spheres and matroid polytopes.

You might also be interested in the following pages by Hiroyuki Miyata:

and Lukas Finschi's "Homepage of Oriented Matroids".

You can find Frank Lutz's lists of simplicial spheres (and other manifolds) here:

Let me shamelessly self-advertise my list of simplicial 4-polytopes with up to $10$ vertices and various families of neighborly polytopes here. I give realization with rational coordinates (inscribed, if possible). You can extract the lists of facets easily from the coordinates. For the simplicial 4-polytopes with 10 vertices I use the same numbering as Frank Lutz uses for the simplicial 3-spheres. Of course some of the spheres are non-realizable ($85\ 878$ to be precise), and then the corresponding number does not appear in my list.

There is an arxiv preprint summarizing the results: Realizability and inscribability for some simplicial spheres and matroid polytopes.

You might also be interested in the following pages by Hiroyuki Miyata:

and Lukas Finschi's "Homepage of Oriented Matroids".

For (simplicial) 3-dimensional polytopes, it is very very fast to generate the combinatorial types of triangulations using plantri, by Gunnar Brinkmann and Brendan McKay, so there really is no need for a database. (At least for polytopes with a small number of vertices. A database of "interesting polytopes" and not "all polytopes up to a certian number of vertices" would still be something nice to have)

Source Link
Moritz Firsching
Moritz Firsching
  • 10.7k
  • 3
  • 63
  • 88

You can find Frank Lutz's lists of simplicial spheres (and other manifolds) here:

Let me shamelessly self-advertise my list of simplicial 4-polytopes with up to $10$ vertices and various families of neighborly polytopes here. I give realization with rational coordinates (inscribed, if possible). You can extract the lists of facets easily from the coordinates. For the simplicial 4-polytopes with 10 vertices I use the same numbering as Frank Lutz uses for the simplicial 3-spheres. Of course some of the spheres are non-realizable ($85\ 878$ to be precise), and then the corresponding number does not appear in my list.

There is an arxiv preprint summarizing the results: Realizability and inscribability for some simplicial spheres and matroid polytopes.

You might also be interested in the following pages by Hiroyuki Miyata:

and Lukas Finschi's "Homepage of Oriented Matroids".