Twofold Translative Tiles in Three-Dimensional Space

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.