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Characterization of the Three-Dimensional Fivefold Translative Tiles
Mei Han, Kirati Sriamorn, Qi Yang +1
This paper proves the following statement: If a convex body can form a fivefold translative tiling in , it must be a parallelotope, a hexagonal prism, a rhombic dodec…
On the multiple illumination numbers of convex bodies
Kirati Sriamorn
In this paper, we introduce an -fold illumination number of a convex body in Euclidean space , which is the smallest number of directions required to…
The Three and Fourfold Translative Tiles in Three-Dimensional Space
Mei Han, Kirati Sriamorn, Qi Yang +1
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 w…
Twofold Translative Tiles in Three-Dimensional Space
Mei Han, Qi Yang, Kirati Sriamorn +1
This paper proves the following statement: {\it If a convex body can form a twofold translative tiling in , it must be a parallelohedron.} In other words, it must be…