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Twofold Translative Tiles in Three-Dimensional Space

2021/06/29 by Mei Han, Qi Yang, Han, Mei +5
Computer Science · Engineering · Materials Science · #Advanced Materials and Mechanics #Cellular Automata and Applications #FOS: Mathematics #Metric Geometry (math.MG) #Quasicrystal Structures and Properties

paper · pdf · doi:10.48550/arxiv.2106.15388

openalex publication_date 2021/06/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper proves the following statement: \it If a convex body can form a twofold translative tiling in 𝔼3, 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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