Let V be a 2-dimensional vector space over the real field R with an affine or indefinite symmetric bilinear form. The infinite dihedral group W can be viewed as a subgroup of GL(V). In the present paper we will classify all crystallographic groups associated with W up to conjugation in the affine group A(V).
Let V be a hyperbolic 5-dimensional indefinite space. W is the infinite Weyl group of an irreducible root system. The principal aim of this paper is to classify all crystallgraphic groups associated with W up to conjugation in the affine group A(V).
