  We define a generalization of Coxeter graphs and an associated Coxeter system
and Coxeter mapping class. These can be used to construct periodic Coxeter
mapping classes on surfaces with arbitrarily large genus, preserving lots of
symmetries. The periodic mapping classes can in turn be used to construct
sequences of pseudo-Anosov mapping classes with bounded normalized dilatation
and arbitrarily high genus. We show that the smallest known accumulation point
of normalized dilatations can be realized by such a sequence.
