A quadrilateral is a polygon having four sides, four angles, and four vertices. A polygon means that the figure is a closed shape, meaning the last line segment connects back to the first one, effectively enclosing an area.
We usually think of quadrilaterals as squares, rectangles, parallelograms, trapezoids, rhombuses, or kites. (I was impressed that my four year-old granddaughter knew the last one, although she called it a diamond!) It could also be irregularly shaped with no name.
However, a polygon may intersect itself.
Click through for a demonstration of a self-intersecting quadrilateral, including the R code you can use to try it out yourself.