Quadrilaterals

Convex quadrilaterals Euler diagram of some types of simple quadrilaterals.

A hierarchical taxonomy of quadrilaterals is illustrated by the figure to the right.

All non-self-crossing quadrilaterals tile the plane by repeated rotation around the midpoints of their edges.

Because the Saturn used quadrilaterals, rather than standard triangles, as its basic polygon, cross platform games had to be completely rewritten to see a Saturn port.

Concave quadrilaterals In a concave quadrilateral, one interior angle is bigger than 180° and one of the two diagonals lies outside the quadrilateral.

Determining congruence of polygons The orange and green quadrilaterals are congruent; the blue is not congruent to them.

Of all convex quadrilaterals with given diagonals, the orthodiagonal quadrilateral has the largest area.

Other properties of convex quadrilaterals *Let exterior squares be drawn on all sides of a quadrilateral.

Quadrilaterals are simple (not self-intersecting) or complex (self-intersecting), also called crossed.

Simple quadrilaterals Any quadrilateral that is not self-intersecting is a simple quadrilateral.

Skew quadrilaterals A non-planar quadrilateral is called a skew quadrilateral.

The dual theorem states that of all quadrilaterals with a given area, the square has the shortest perimeter.

The regular octahedron is a special case in which all three quadrilaterals are planar squares.

This is also true for all parallelograms, but not for all quadrilaterals.

This is called the isoperimetric theorem for quadrilaterals.

This is true in convex, concave and crossed quadrilaterals provided the area of the latter is defined to be the difference of the areas of the two triangles it is composed of.