Twofold Translative Tiles in Three-Dimensional Space

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.

References in corpus (1)

• Characterization of the Two-Dimensional Six-Fold Lattice Tiles