Bezdek A. (Ed.) Discrete Geometry

N.-Y.: Marcel Dekker, 2003. — 486 p. — (Monographs and Textbooks in Pure and Applied Mathematics 253). — ISBN: 0-8247-0968-3.Celebrating the work of Professor W. Kuperberg, this reference explores packing and covering theory, tilings, combinatorial and computational geometry, and convexity, featuring an extensive collection of problems compiled at the Discrete Geometry Special Session of the AMS in New Orleans, Louisiana. Discrete Geometry analyzes packings and coverings with congruent convex bodies , arrangements on the sphere, line transversals, Euclidean and spherical tilings, geometric graphs, polygons and polyhedra, and fixing systems for convex figures. This text also offers research and contributions from more than 50 esteemed international authorities, making it a valuable addition to any mathematical library.Transversal lines to lines and intervals
On a shortest path problem of G. Fejes Toth
A short survey of (r, ^-structures
Lattice points on the boundary of the integer hull
The Erdos-Szekeres problem for planar points in arbitrary position
Separation in totally-sewn 4-polytopes
On a class of equifacetted polytopes
Chessboard Ramsey numbers
Maximal primitive fixing systems for convex figures
The Newton-Gregory problem revisited
Arrangements of 13 points on a sphere
On point sets without k collinear points
The Beckman-Quarles theorem for rational d-spaces, d even and d > 6
Edge-antipodal convex polytopes - a proof of Talata's conjecture
Single-split tilings of the sphere with right triangles
Vertex-unfoldings of simplicial manifolds
View-obstruction through trajectories of co-dimension three
Fat 4-polytopes and fatter 3-spheres
Arbitrarily large neighborly families of congruent symmetric convex 3-polytopes
On the non-solidity of some packings and coverings with circles
On the mth Petty numbers of normed spaces
Cubic polyhedra
"New" uniform polyhedra
On the existence of a convex polygon with a specified number of interior points
On-line 2-adic covering of the unit square by boxes
An example of a stable, even order quadrangle which is determined by its angle function
Sets with a unique extension to a set of constant width
The number of simplices embracing the origin
Helly-type theorems on definite supporting lines for /c-disjoint families of convex bodies in the plane
Combinatorial aperiodicity of polyhedral prototiles
Sequences of smoothed polygons
On a packing inequality by Graham, Witsenhausen and Zassenhaus
Covering a triangle with homothetic copies
Open Problems