Twofold Translative Tiles in Three-Dimensional Space

Mei Han; Qi Yang; Kirati Sriamorn; Chuanming Zong

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arXiv · 2106.15388

Twofold Translative Tiles in Three-Dimensional Space

Mei Han·Qi Yang·Kirati Sriamorn·Chuanming Zong

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Abstract

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.

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Mei Han, Qi Yang, Kirati Sriamorn, Chuanming Zong. 2021-06-29. Twofold Translative Tiles in Three-Dimensional Space. https://arxiv.org/abs/2106.15388

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