A Euclidean polygon with four sides and four right angles. Opposite sides are parallel and have equal lengths. A rectangle is a square exactly when its adjacent side lengths agree.
A rectangle with all four side lengths equal. It is a regular four-sided polygon. Rotations and translations preserve this definition; its sides need not be parallel to the coordinate axes.
A square frame formed by removing a concentric square hole from a larger square. If outer and inner sides are positive integers with the same integer parity, the border has integer thickness and contains unit tiles.