Geometry is a classical core part of mathematics which, with its birth,
marked the beginning of the mathematical sciences. Thus, not
surprisingly, geometry has played a key role in many important
developments of mathematics in the past, as well as in present times.
While focusing on modern mathematics, one has to emphasize the
increasing role of discrete mathematics, or equivalently, the broad
movement to establish discrete analogues of major components of
mathematics. In this way, the works of a number of outstanding mathema-
cians including H. S. M. Coxeter (Canada), C. A. Rogers (United
Kingdom), and L. Fejes-T oth (Hungary) led to the new and fast
developing eld called discrete geometry. One can brie y describe this
branch of geometry as the study of discrete arrangements of geometric
objects in Euclidean, as well as in non-Euclidean spaces. This, as a
classical core part, also includes the theory of polytopes and tilings
in addition to the theory of packing and covering. D- crete geometry is
driven by problems often featuring a very clear visual and applied
character. The solutions use a variety of methods of modern mat- matics,
including convex and combinatorial geometry, coding theory, calculus of
variations, di erential geometry, group theory, and topology, as well as
geometric analysis and number theory.
