English: Derivation of the Kelvin geometry from bio-inspired aluminum foam (a); model of a 3D Kelvin cell (b); and Kelvin-inspired honeycomb geometry (c). Derivation of Weaire-inspired honeycomb from segments of Weaire Phelan structures (d) and interpretations onto a two-dimensional (2D) plane that allows it to be connected with similar geometries in a Weaire-inspired unit cell (e). Relationships between graph pairs, geometries whose intersections of nodes match pre-existing geometries of known honeycombs: Triangular, hexagonal, and Kagome (f, g, and h) are all paired to triangular cells, while Pomelo and spiderweb are paired to spiderweb (i and j). K shows the derivation of floret from a hierarchical honeycomb