  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.
