Fig. 2.

Entangled colloidal aggregates show alternating colored domains, delimited by the disclinations. (A) The grid does not have to be rectangular to construct the graph. The cell in C has an opposite handedness compared with A and B. (A, Inset) Interface between chiral domains of opposite handedness. A λ-plate oriented at $45°$ to both polarizer and analyzer reveals the domains in different colors. The colored domains map directly to the nodes of the medial graph. (C) The resulting signed planar graph can be further simplified with the graph version of the Reidemeister moves and used to recognize the knot. (D, Inset) The graph edges are labeled as “+” or “−” according to the type of crossing they represent. The structures in the panels are the figure-eight knot $\left(4_1\right)$, the trefoil knot $\left(3_1\right)$, and the Borromean rings $\left(6_2^3\right)$, respectively.