Structures - Not the Tiles, but the Joints
Abstract
M.C. Escher made about 150 basic drawings of regular divisions, some of which were used later in his prints. Tiles should fit tightly together on all sides, so that there is no space between them. In other words, the joint separates them in practice, but can theoretically be reduced to nothing. Mathematicians would call these joints "edges" of the tiling; edges are never considered to have any width. We can say that this is the mathematical point of view. From an artistic point of view, the separating-lines between tiles will always be there; we can’t ignore them. We can give these boundaries more attention and even go so far as to omit the tiles. What we have then is just a grid of joints, connected in some regular way, or a latticework: a plane with a lot of carefully outlined holes.

Paper published in M.C. Escher's Legacy, Springer, 2003

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