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The polymake database
There is a database with polymake objects.
The data can be accessed from within polymake via the extension poly_db. It can also be viewed via a web browser.
Here is a list of the current content of the database. There are two levels of hierarchy: Databases and collections.
| Database | Collection | |
|---|---|---|
| LatticePolytopes | SmoothReflexive | All smooth reflexive lattice polytopes in dimensions up to 8. In dimensions up to 7 the database contains the properties H_STAR_VECTOR, REFLEXIVE, CONE_DIM, date, _id, LATTICE_CODEGREE, N_INTERIOR_LATTICE_POINTS, SMOOTH, N_LATTICE_POINTS, FACET_WIDTHS, VERTICES, FACETS, CENTROID, N_VERTICES, contributor, LATTICE_DEGREE, LATTICE_VOLUME, EHRHART_POLYNOMIAL_COEFF, N_BOUNDARY_LATTICE_POINTS, ESSENTIALLY_GENERIC, VERY_AMPLE, F_VECTOR, GORENSTEIN, FEASIBLE, LINEALITY_SPACE, AFFINE_HULL. In dimension 8 it only contains the minimal set LINEALITY_SPACE, CONE_DIM, date, _id, VERTICES, FEASIBLE, N_VERTICES, contributor. |
| LatticePolytopesR | SmoothReflexive | All smooth reflexive lattice polytopes in dimension 8. (Properties are still incomplete!) Note that you need a password to access this database. |
| Tropical | TOM | All known non-realisable tropical oriented matroids with parameters n=6, d=3 or n=d=4. You need the extension tropmat for this. |
Other data in polymake format
This is a collection of objects from geometric combinatorics available in polymake format.
- Katja Kulas: list of all 3-dimensional polytropes.
- Sven Herrmann, Anders Jensen, Michael Joswig, and Bernd Sturmfels: list of Generic planes in tropical projective space TP5 and TP6.
- Debbie Grier, Peter Huggins, Bernd Sturmfels, and Josephine Yu: list of triangulations of the 4-cube.
- Mikkel Øbro; Benjamin Lorenz, Andreas Paffenholz: Smooth reflexive lattice polytopes in dimensions up to 9
- Barbara Baumeister, Christian Haase, Benjamin Nill, and Andreas Paffenholz: low-dimensional permutation polytopes
- Andreas Paffenholz: Various lists of polytopes
- Katrin Herr and Thomas Rehn: 2-homogeneous groups up to degree 12 and orbit polytopes of representatives of all their core points.
You can also check here for other classes of polytopes.
Contributions are welcome!