TITLE: Decidability of tiling of $\mathbb{R}^n$
QUESTION [7 upvotes]: Given a polytope of dimension $n$, is there some general way to determine if it can tile $\mathbb{R}^n$?

REPLY [6 votes]: The book Tilings and Patterns by Branko Grünbaum and Geoffrey Shephard (W.H. Freeman) is still, despite its 1987 publication date, an excellent source of information about tiling questions. Wang tiles and decidability problems are treated in Chapter 11.