Chapter 1 introduces some of the terminology and notation used later and
indicates prerequisites. Chapter 2 gives a reasonably thorough account
of all finite subgroups of the orthogonal groups in two and three
dimensions. The presentation is somewhat less formal than in succeeding
chapters. For instance, the existence of the icosahedron is accepted as
an empirical fact, and no formal proof of existence is included.
Throughout most of Chapter 2 we do not distinguish between groups that
are "geo- metrically indistinguishable," that is, conjugate in the
orthogonal group. Very little of the material in Chapter 2 is actually
required for the sub- sequent chapters, but it serves two important
purposes: It aids in the development of geometrical insight, and it
serves as a source of illustrative examples. There is a discussion
offundamental regions in Chapter 3. Chapter 4 provides a correspondence
between fundamental reflections and funda- mental regions via a
discussion of root systems. The actual classification and construction
of finite reflection groups takes place in Chapter 5. where we have in
part followed the methods of E. Witt and B. L. van der Waerden.
Generators and relations for finite reflection groups are discussed in
Chapter 6. There are historical remarks and suggestions for further
reading in a Post lude.
