Explore the intricate connections between geometry, statistical mechanics, and integrability in this advanced lecture presented at UCLA's Institute for Pure & Applied Mathematics. Delve into the second part of Marianna Russkikh's presentation, focusing on geometric embeddings of underlying dimer graphs and their algebra-combinatorial properties. Gain insights from the University of Notre Dame researcher as she expands on the concepts introduced in the first part of the series. Enhance your understanding of complex mathematical concepts and their applications in this 80-minute recorded session from IPAM's Geometry, Statistical Mechanics, and Integrability Tutorials.