Crossed Rectangles
A crossed (self-intersecting) quadrilateral 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. A three-dimensional rectangular wire frame that is twisted can take the shape of a bow tie. A crossed rectangle is sometimes called an "angular eight".
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 is not equiangular. The sum of its interior angles (two acute and two reflex), as with any crossed quadrilateral, is 720°.
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°).
Read more about this topic: Rectangle
Famous quotes containing the word crossed:
“A slight digression: that bit about my mother was a deliberate lie. In reality, she was a woman of the people, simple and coarse, sordidly dressed in a kind of blouse hanging loose at the waist. I could, of course, have crossed it out, but I purposely leave it there as a sample of one of my essential traits: my light-hearted, inspired lying.”
—Vladimir Nabokov (1899–1977)