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