Supersymmetry from superspace to graph theory and polyhedra: <i>Celebrationum scripta collecta</i>

We review a variety of mathematical structures underlying supersymmetry, ranging from the description of gauge theories and gravity in Superspace to the combinatorial and graph-theoretic frameworks that capture the algebraic content of its representations. The discussion revisits how geometric notions commonly associated with manifestly supersymmetric gauge theories can emerge rather than being assumed a priori. This exploration is followed by an extensive treatment of supersymmetry representations through the lens of combinatorics, higher-dimensional polytopes and graph theory. The synthesis of these perspectives shows that supersymmetry, far from being confined to a single language, builds bridges to seemingly unrelated domains of mathematics and finds expression in multiple guises, each offering complementary insights into its structure.