English

Twofold Translative Tiles in Three-Dimensional Space

Metric Geometry 2021-06-30 v1

Abstract

This paper proves the following statement: {\it If a convex body can form a twofold translative tiling in E3\mathbb{E}^3, it must be a parallelohedron.} In other words, it must be a parallelotope, a hexagonal prism, a rhombic dodecahedron, an elongated dodecahedron, or a truncated octahedron.

Keywords

Cite

@article{arxiv.2106.15388,
  title  = {Twofold Translative Tiles in Three-Dimensional Space},
  author = {Mei Han and Qi Yang and Kirati Sriamorn and Chuanming Zong},
  journal= {arXiv preprint arXiv:2106.15388},
  year   = {2021}
}