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.

These tickets have been merged in version 8.0.beta1. 
See https://trac.sagemath.org/ticket/22710 for a meta-ticket that is 
tracking polymake-related development.

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.


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