English

Concrete polytopes may not tile the space

Metric Geometry 2021-04-16 v2 Combinatorics Number Theory

Abstract

Brandolini et al. conjectured that all concrete lattice polytopes can multitile the space. We disprove this conjecture in a strong form, by constructing an infinite family of counterexamples in R3\mathbb{R}^3.

Keywords

Cite

@article{arxiv.2003.04667,
  title  = {Concrete polytopes may not tile the space},
  author = {Alexey Garber and Igor Pak},
  journal= {arXiv preprint arXiv:2003.04667},
  year   = {2021}
}

Comments

6 pages

R2 v1 2026-06-23T14:10:00.396Z