Cox and Group Theory

Coxeter groups are mathematical structures that describe symmetrical patterns and transformations, often visualized as reflections like mirrors across lines or planes. They help classify and analyze symmetrical objects in geometry. Group theory, more broadly, studies sets equipped with an operation (like addition or multiplication) that combines elements while satisfying specific rules (closure, associativity, identity, inverses). Together, Coxeter groups are a special kind of group focused on reflection symmetries. Understanding these concepts aids in various fields like crystallography, art, and physics by providing a framework to analyze how symmetry shapes structures and patterns.