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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).
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rectangle
