Twofold Translative Tiles in Three-Dimensional Space
Mei Han, Qi Zhi Yang, Kirati Sriamorn, Chuanming Zong · arXiv (Cornell University) · 2021
This paper proves the following statement: {\it If a convex body can form a twofold translative tiling in $\mathbb{E}^3$, 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.