Coxeter Group

A Coxeter group is a mathematical concept describing symmetries generated by reflections, like flipping or mirroring across lines or planes. Imagine a set of mirrors arranged in specific ways, where each reflection produces a symmetrical pattern. These groups are defined by simple rules about how these reflections combine—specifically, how many times you need to apply certain reflections to return to the starting position. Coxeter groups help mathematicians understand complex symmetrical structures, including crystal patterns, regular polyhedra, and abstract geometric objects, by providing an algebraic framework for analyzing their symmetrical properties.