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Finite arrangements of convex bodies were intensively investigated
in the second half of the twentieth century. Connections to many
other subjects were made, including crystallography, the local
theory of Banach spaces, and combinatorial optimisation. This book,
the first one dedicated solely to the subject, provides an in-depth
state-of-the-art discussion of the theory of finite packings and
coverings by convex bodies. It contains various new results and
arguments, besides collecting those scattered around in the
literature, and provides a comprehensive treatment of problems
whose interplay was not clearly understood before. In order to make
the material more accessible, each chapter is essentially
independent, and two-dimensional and higher-dimensional
arrangements are discussed separately. Arrangements of congruent
convex bodies in Euclidean space are discussed, and the density of
finite packing and covering by balls in Euclidean, spherical and
hyperbolic spaces is considered.
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