polyrectangles

Polyrectangles are a type of polyomino, which are geometric shapes formed by connecting equal-sized squares edge-to-edge. Specifically, a polyrectangle is a polyomino that can be arranged into a solid rectangle. The smallest polyrectangles are the monorectangle (a single square), the two-by-one rectangle (a domino), and the two-by-two square (a tetromino). As the number of squares increases, so does the variety of polyrectangles. For example, a set of six squares can form a 1x6, 2x3, or 3x2 rectangle. Therefore, a polyrectangle with n squares is a shape that can tile an n-square rectangle, and conversely, an n-square rectangle can be dissected into a specific polyrectangle. The study of polyrectangles is related to tiling problems and recreational mathematics. Determining which numbers of squares can form polyrectangles that tile rectangles of specific dimensions is a common puzzle. For instance, it is impossible to tile a 3x4 rectangle with 12 monominoes. The term "polyrectangle" emphasizes the rectangular form that the constituent squares can create.