A well-known tiling of the plane employs offset square tiles of two sizes. See the example below using tiles of 2 and 3 units, somewhat perturbed on this occasion by proportional spacing rather than incompetent home improvement skills. [ * * * * * * * * * ] [ * * * * * * * * * ] [ * * * * * * * * * ] [ * * * * * * * * ] [ * * * * * * * * ] [ * * * * * * * * * ] [ * * * * * * * * ] [ * * * * * * * * * ] [ * * * * * * * * ] [ * * * * * * * * ] [ * * * * * * * * * ] [ * * * * * * * * * ] [ * * * * * * * * * ] [ * * * * * * * * * ] I can't resist remarking that such diagrams provide a particularly elegant demonstration of Pythagoras' theorem, apparent when the period along a horizontal axis is calculated. A particularly humiliating programming exercise involves generating a matrix in which unoccupied cells above are represented by 0 and asterisked cells by +1 or -1 , chosen to satisfy the local constraints on an integer number wall (frame theorems). But all that's completely irrelevant to my purpose, which is simply to enquire if these tilings have an established name --- preferably one rather more euphonious than my current nomenclature: The bathroom floor tiling! Fred Lunnon