Editing Rectangle (section)

==Crossed rectangles==
A [[list of self-intersecting polygons|''crossed'']] ''quadrilateral'' (self-intersecting) consists of two opposite sides of a non-self-intersecting quadrilateral along with the two diagonals. Similarly, a crossed rectangle is a ''crossed quadrilateral'' which consists of two opposite sides of a rectangle along with the two diagonals. It has the same [[vertex arrangement]] as the rectangle. It appears as two identical triangles with a common vertex, but the geometric intersection is not considered a vertex.

A ''crossed quadrilateral'' is sometimes likened to a [[bow tie]] or [[butterfly]], sometimes called an "angular eight". A [[three-dimensional]] rectangular [[wire]] [[Space frame|frame]] that is twisted can take the shape of a bow tie.

The interior of a ''crossed rectangle'' can have a [[polygon density]] of ±1 in each triangle, dependent upon the winding orientation as clockwise or counterclockwise.

A ''crossed rectangle'' may be considered [[equiangular polygon|equiangular]] if right and left turns are allowed. As with any ''crossed quadrilateral'', the sum of its [[interior angle]]s is 720°, allowing for internal angles to appear on the outside and exceed 180°.<ref>[https://web.archive.org/web/20150723004135/http://mysite.mweb.co.za/residents/profmd/stars.pdf Stars: A Second Look]. (PDF). Retrieved 2011-11-13.</ref>

A rectangle and a crossed rectangle are quadrilaterals with the following properties in common:
* Opposite sides are equal in length.
* The two diagonals are equal in length.
* It has two lines of reflectional symmetry and rotational symmetry of order 2 (through 180°).

[[File:Crossed rectangles.png|320px]]