The Finite Reflection Group H_4

The reflection group H_4 encodes the symmetries of the regular poly-tope 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 re-flection 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 com-pared. 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 buil-ding 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 non-crystallographic groups.