This chapter introduced algebraic formulations as an innovative approach to 2DGS and 3DGS. These formulations capture the essence of the reciprocal relationship, representing the dual diagram algebraically. While requiring deeper insight into reciprocity, this method surpasses traditional approaches in its potency. With the aid of modern computational tools, we can efficiently navigate the solution space of these equations. The resultant algebraic framework promises increased efficiency, flexibility, and precision, enhancing our understanding of the relationship between form and force. Such advancements prove invaluable not only for academic pursuits but also for practical applications.

The method of Algebraic graphic statics comes with certain limitations. Primarily, it’s suited for linear static issues and linear constraints. Handling more intricate problems, such as the previously mentioned constraints on face areas, might not be straightforward. Such challenges may require quadratic functions, increasing the computational effort and cost for solutions. In terms of the implementation, although the data structure allows self-intersecting faces and cells to exist through later manipulation, the initial construction of the data structure cannot accept self-intersecting surfaces, i.e., all cells in the starting primal diagram need to be convex; otherwise, the topology cannot be detected and defined properly.

We invite the interested reader to visit other related topics under graphic statics, including vector-based 3D graphic statics \cite{Cremona1890,EPFL-CONF-218827,D'Acunto_2019}, and approaches using projections of polyhedral systems to higher dimensions and back by \cite{Konstantatou} and \cite{Baranyai2021}. Furthermore, \cite{Lee2018} proposed a method called \textit{Disjointed Force Polyhedra} where the equilibrium of the system was computed by constructing a single convex polyhedron for each node using Extended Gaussian Image algorithm, and then areas of the adjacent faces have matching areas but are allowed to have different shapes \cite{Lee2018,Lee2018phd}. In \cite{mcrobie_2016_minkowski}, a methodology was introduced for the computation and visualization of the Maxwell (in two dimensions) and Rankine (in three dimensions) diagrams that are reciprocal to a truss subjected to load. The formulation of these reciprocals is grounded in the Minkowski summation of the polyhedral stress functions inherent to both the original and the reciprocal diagrams. This approach aligns seamlessly with 3D graphic statics that utilize polyhedral reciprocal diagrams.