The Finite Reflection Group H_4

The reflection group H_4 encodes the symmetries of the regular poly­tope called the 600-cell which is a four-dimensional analogue of the icosahedron. The structure of H_4 has many interesting relations to a variety of topics of mathematics and physics.This book outlines the ideas behind the classification of finite re­flection groups giving a context for H_4 as the largest exceptional noncrystallographic reflection group. Different constructions of H_4 and its root system which have thus far been published in pieces throughout the mathematics literature are then described and com­pared. The book also examines a construction of the character table of H_4 which uses information about the group and root system structure. Finally an algorithm which gives a systematic way of buil­ding character tables for any finite group is described.This book would be useful for anyone interested in finite reflection groups especially those whose interests lie in the study of non­crystallographic groups.