TITLE: Name this periodic tiling
QUESTION [10 upvotes]: I've been working on a problem I'm working on in ergodic theory (finding Alpern lemmas for measure-preserving $\mathbb R^d$ actions) and have found some neat tilings, that I presume were previously known. 
They are periodic tilings of $\mathbb R^d$ by a single prototile consisting of any box with a smaller box removed from a corner. The two-dimensional case is illustrated in the figure below:

There exist versions of this in arbitrary dimensions, irrespective of the size of the boxes. Furthermore, there appear to be many essentially different tilings using the same prototile. 

Does anybody recognize the $d$-dimensional version, or have a name for it?

Thanks

REPLY [5 votes]: Kolountzakis worked with some tilings of this sort in his paper "Lattice tilings by cubes: whole, notched and extended", Electr. J. Combinatorics 5 (1998), 1, R14.