  Automating the solutions of multiple network information theory problems,
stretching from fundamental concerns such as determining all information
inequalities and the limitations of linear codes, to applied ones such as
designing coded networks, distributed storage systems, and caching systems, can
be posed as polyhedral projections. These problems are demonstrated to exhibit
multiple types of polyhedral symmetries. It is shown how these symmetries can
be exploited to reduce the complexity of solving these problems through
polyhedral projection.
