The main feature of our classification is that it contains degenerate cases.

Each line of the files contains exactly one oriented matroid, reprensented by the RevLex-Index encoding of its chirotope,

which is used in the database of oriented matroids by Finschi and Fukuda.

- realizable oriented matroids in OM(4,8) (zip file 567KB, original file 13MB)
- realizable oriented matroids in OM(3,9) (zip file 1.49MB, original file 38MB)
- realizable oriented matroids in OM(6,9) (zip file 1.62MB, original file 42MB)
- non-realizable oriented matroids in OM(4,8) (zip file 14.1KB, original file 276KB)
- non-realizable oriented matroids in OM(3,9) (zip file 1.39KB, original file 23KB)
- non-realizable oriented matroids in OM(6,9) (zip file 1.32KB, original file 23KB)

Realizations for OM(6,9) are not uploaded since one can check realizability of OM(6,9) easily from the result of OM(3,9).

If you would also like to get realizations for OM(6,9), please contact the authors.

- realizations of realizable oriented matroids in OM(4,8) (zip file 8.2MB, original file 62MB) (matrix representation ver.)
- realizations of realizable oriented matroids in OM(3,9) (zip file 21MB, original file 153MB) (matrix representation ver.)
- README

Final polynomials for OM(6,9) are not uploaded since one can check non-realizabilty of OM(6,9) easily from the result of OM(3,9).

Please constact the authors if you would also like to get data of final polynomials for OM(6,9).

- final polynomials of non-realizable oriented matroids in OM(4,8) (zip file 388KB, original file 3.98MB)
- final polynomials of non-realizable oriented matroids in OM(3,9) (zip file 42KB, original file 359KB)
- README

We adopt the RevLex-Index encodings of chirotopes to represent combinatorial types.

Each line of the files contains exactly one combinatorial type.

- 3-dimensional point configurations on 8 points (zip file 77.6MB, original file 715MB)
- 2-dimensional point configurations on 9 points (zip file 110MB, original file 1.3GB)
- 5-dimensional point configurations on 9 points (zip files: toal 828MB, original files: toal 8.53GB) file1 file2 file3 file4 file5

Each line of the file contains exactly one face lattice represented by the facet list,

where each bracket corresponds to facet.

- 3-dimensional polytopes with 4 vertices (text file)
- 3-dimensional polytopes with 5 vertices (text file)
- 3-dimensional polytopes with 6 vertices (text file)
- 3-dimensional polytopes with 7 vertices (text file)
- 3-dimensional polytopes with 8 vertices (text file)
- 4-dimensional polytopes with 5 vertices (text file)
- 4-dimensional polytopes with 6 vertices (text file)
- 4-dimensional polytopes with 7 vertices (text file)
- 4-dimensional polytopes with 8 vertices (text file)
- 5-dimensional polytopes with 6 vertices (text file)
- 5-dimensional polytopes with 7 vertices (text file)
- 5-dimensional polytopes with 8 vertices (text file)
- 5-dimensional polytopes with 9 vertices (zip file 459KB, original file 11MB)
- 6-dimensional polytopes with 7 vertices (text file)
- 6-dimensional polytopes with 8 vertices (text file)
- 6-dimensional polytopes with 9 vertices (text file)
- 7-dimensional polytopes with 8 vertices (text file)
- 7-dimensional polytopes with 9 vertices (text file)

- Homepage of Oriented Matroids by Lukas Finschi.
- Enumerating Order Types for Small Point Sets with Applications by Oswin Aichholzer.
- Database of Matroids by Yoshitake Matsumoto.
- Database of Combinatorially Different Line Arrangements by Tobias Christ.
- The Manifold page by Frank H. Lutz.

A large database of oriented matroids including degenerate ones. Our page is based on this page.

A large database of point configurations in general position.

You can also find various kinds of applications of the database in their works.

A large database of matroids. This database also covers rank-5 matroids with 10 elements.

A large database of simple line arrangements based on Aichholzer's database of order types. You can enjoy many pictures there.

A large database of triangulated manifolds. You can find many interesting examples in discrete differential geometry there.

Please feel free to contact the authors. Hiroyuki Miyata (hmiyata AT is DOT s DOT u-tokyo DOT ac DOT jp)

Sonoko Moriyama (moriso AT dais DOT is DOT tohoku DOT ac DOT jp)

Komei Fukuda (fukuda AT ifor DOT math DOT ethz DOT ch)