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Twofold Translative Tiles in Three-Dimensional Space
Published 29 Jun 2021 in math.MG | (2106.15388v1)
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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