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This is crossposted from MSE. We say a subset $A$ of a group $G$ is a monotile for $G$ if $G$ is a disjoint union of right translates of $A$. In his article Monotileable Amenable Groups, B. Weiss ...

This is perhaps a vague question, but hopefully there exists literature on the subject. The question is motivated by an answer I gave to this question on math.SE. There exists a rather remarkable ...