Coxeter Groups: Classification and Exceptional Construction

This lecture covers the classification of irreducible crystallographic Coxeter groups, explaining how to determine a Coxeter group in R^3 from its Coxeter graph. It also delves into the construction of exceptional Coxeter groups through the method of choosing vectors with specific angles and lengths determined by the Coxeter graph and crystallographic conditions, followed by generating the group using simple reflections and constructing it inductively. The lecture concludes with the termination process for all indecomposable Coxeter graphs.