Rectangle

A closed planar quadrilateral with opposite sides of equal lengths and , and with four right angles. A square is a degenerate rectangle with .

The area of the rectangle is

(1)

and its polygon diagonals and are of length

(2)

A rectangle has a circumcircle with circumradius

(3)

but incircle only in the degenerate case of a square.

A number of important topological surfaces can be constructed from the rectangle. Gluing both pairs of opposite edges together with no twists gives a torus, gluing two opposite edges together after giving a half-twist gives a Möbius strip, gluing both pairs of opposite edges together giving one pair a half-twist gives a Klein bottle, and giving both pairs a half-twist gives a projective plane (Stewart 1997).