What is known about unit cubes

@article{Zong2005WhatIK,
  title={What is known about unit cubes},
  author={Chuanming Zong},
  journal={Bulletin of the American Mathematical Society},
  year={2005},
  volume={42},
  pages={181-211}
}
  • C. Zong
  • Published 26 January 2005
  • Computer Science
  • Bulletin of the American Mathematical Society
Unit cubes, from any point of view, are among the simplest and the most important objects in n-dimensional Euclidean space. In fact, as one will see from this survey, they are not simple at all. On the one hand, the known results about them have been achieved by employing complicated machineries from Number Theory, Group Theory, Probability Theory, Matrix Theory, Hyperbolic Geometry, Combinatorics, etc.; on the other hand, the answers for many basic problems about them are still missing. In… 
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