Coxeter

Coxeter is a surname most commonly associated with the British geometer Harold Scott MacDonald Coxeter (1905–2003). Born in Canada, he became a leading figure in geometry after moving to the United Kingdom. Coxeter made major contributions to the study of polyhedra, tilings, and symmetry, and he helped develop the modern theory of reflection groups and the notation now known as Coxeter groups and Coxeter–Dynkin diagrams. He authored several influential works on geometry and polytopes that shaped the field.

In mathematics, a Coxeter group is a group generated by reflections in a Euclidean or more general vector space, with relations determined by a symmetric matrix of integers. Finite Coxeter groups correspond to finite reflection groups and are classified by Coxeter–Dynkin diagrams of types A, B, D, E, F, G, H and I. Examples include the symmetric groups S_n (type A_{n-1}) and dihedral groups (type I_2(m)). These groups arise in the study of root systems, Lie algebras, and regular polytopes.

The term also appears in related concepts such as Coxeter numbers and Weyl groups; the subject has broad applications in geometry, algebra, combinatorics, and mathematical physics.