The Three and Fourfold Translative Tiles in Three-Dimensional Space
arXiv:2109.07116
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.
arXiv commentarXiv admin note: text overlap with arXiv:2106.15388
References in corpus (5)
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- Twofold Translative Tilings with Convex Bodies
- Characterization of the Two-Dimensional Six-Fold Lattice Tiles