polyDB is a database for objects in discrete geometry and related areas. The database can be accessed from within polymake or via a REST API. There is also a web interface at db.polymake.org. Internally, the database is build upon MongoDB, and you can use the full MongoDB query language to send requests to the database.

• tutorial for querying the database
• (Experimental) polyDB REST API

This is a collection of objects from geometric combinatorics available in polymake format.

• Bernd Sturmfels and Josephine Yu: tight spans of triangulations and coarsest subdivisions of hypersimplex Delta(2,6) (note: link currently broken).
• Sven Herrmann, Anders Jensen, Michael Joswig, and Bernd Sturmfels: list of Generic planes in tropical projective space TP5 and TP6 (note: links currently broken).
• Debbie Grier, Peter Huggins, Bernd Sturmfels, and Josephine Yu: list of triangulations of the 4-cube (note: link currently broken).
• 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
• Boris Springborn: gallery of polyhedral types
• 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.

• Lars Kastner, Robert Löwe: Regular triangulations of the 3-dilated 3-simplex
• Lena Weis: Some Schlaefli fans, this data is accompanied by the code at dmg-lab on github.

Contributions are welcome!