Translational tilings by a polytope, with multiplicity

• Main Authors: Robins, Sinai., Shiryaev, Dmitry., Gravin, Nick.
• Other Authors: School of Physical and Mathematical Sciences
• Format: Article
• Language: English
• Published: 2013
• Online Access: https://hdl.handle.net/10356/96779; http://hdl.handle.net/10220/13087
• Institution: Nanyang Technological University

We study the problem of covering Rd by overlapping translates of a convex polytope, such that almost every point of Rd is covered exactly k times. Such a covering of Euclidean space by a discrete set of translations is called a k-tiling. The investigation of simple tilings by translations (which...