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The Three and Fourfold Translative Tiles in Three-Dimensional Space
Published 15 Sep 2021 in math.MG | (2109.07116v2)
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.
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