3 papers
math.MG2021
Cubes and Boxes have Rupert's passages in every direction
András Bezdek, Zhenyue Guan, Mihály Hujter +1
It is a year old counterintuitive observation of Prince Rupert of Rhine that in cube a straight tunnel can be cut, through which a second congruent cube can be passed. Hundre…
math.MG2021
Separating circles on the sphere by polygonal tilings
Andras Bezdek
We say that a tiling separates discs of a packing in the Euclidean plane, if each tile contains exactly one member of the packing. It is a known elementary geometric problem to sho…
math.MG2010
Dense packing of space with various convex solids
András Bezdek, Włodzimierz Kuperberg
One of the basic problems in discrete geometry is to determine the most efficient packing of congruent replicas of a given convex set in the plane or in space. The most commonl…