polymake (
https://polymake.org/doku.php) is an excellent, mature, and actively maintained open source system for interactive computations in polyhedral geometry (and matroids, tropical geometry, ...), developed since 1997 by Ewgenij Gawrilow and Michael Joswig and various contributors (
https://polymake.org/doku.php/team).
Thanks to the work by Simon King during Sage Days 84 (
https://wiki.sagemath.org/days84), there is now a pexpect-based interface to polymake in Sage. The spkg for polymake is also up to date, packaging the recently released version 3.1. Several follow-up tickets have added data conversion to polymake objects via polymake(x) and from polymake objects via x.sage(); and a backend for the Polyhedron class using polymake. The latter, in particular, offers fast computations for polyhedra over quadratic fields.
Now users and developers are needed who help to integrate polymake's features fully into Sage. With little effort, Sage can now become the go-to system for polyhedral computation (and perhaps other areas such as tropical geometry); on the other hand, Sage will help expand the user base of polymake by introducing the powerful features that polymake offers to a new set of users.