Explore a lecture on the topology of complexes in distributed computing models. Delve into various simplicial models, focusing on iterated chromatic subdivisions and their applications. Examine the Weak Symmetry Breaking example to understand how distributed computing questions translate into combinatorial-simplicial problems. Discover how this approach generates intriguing new questions across multiple mathematical fields. Learn about input and output complexes, protocol complexes, standard chromatic subdivisions, special order partitions, and permutations. Investigate Schlegel diagrams, snapshot protocols, one-round execution, and view complexes. Gain insights into the intersection of algebraic topology and distributed computing through this comprehensive exploration of complex topological structures and their practical implications.