Polyhedral Computations With polymake

This is part of the Hands-on Course on Geometric Software of the Intensive Research Program on Discrete, Combinatorial and Computational Geometry, Barcelona, April 30 - May 4, 2018.


We will start with an introduction to computations in high-dimensional polyhedral geometry, with applications to, e.g., optimization and tropical geometry. Then we will review several algorithms for computing convex hulls and survey their advantages and disadvantages by analyzing explicit examples. The course will end with some reports about and computations near the current frontiers of polyhedral computation.

"Hands-on" means that this is a highly interactive event. The participants will work on lots of exercises.


There will be three sessions of two hours each. Each session will feature some introductory presentation, followed by exercises; see below. We will start at 9:00am sharp!

Exercises [PDF] and Additional Material

The list exercises is now complete. You will find hints to some solutions in the Jupyter notebooks and polymake tutorial code below.

Technical Preparations

Please bring your own laptop with polymake installed as described here, preferably the most recent version 3.2. MacOS users should read and follow this specific advice. If you should be running any flavor of Windows it is recommended that you use the docker image; alternatively you can use the Linux subsystem in Windows 10. As the very last resort there is a web service, but this comes with many restrictions. For instance, it does not give you the many pretty pictures that I will show.



Unfold some polytopes in MatchTheNet.

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Last modified: Son Sep 15 09:08:52 UTC 2019 by mic