The Three and Fourfold Translative Tiles in Three-Dimensional Space
Metric Geometry
2021-10-01 v2
Abstract
This paper proves the following statement: If a convex body can form a three or fourfold translative tiling in the three-dimensional space, 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.2109.07116,
title = {The Three and Fourfold Translative Tiles in Three-Dimensional Space},
author = {Mei Han and Kirati Sriamorn and Qi Yang and Chuanming Zong},
journal= {arXiv preprint arXiv:2109.07116},
year = {2021}
}
Comments
arXiv admin note: text overlap with arXiv:2106.15388