when a quadrilateral is crossed over, so which means one line is crossed over another line then joins to make the shape.
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A complex quadrilateral is not a recognised term. The only suggestion that I can offer is of a quadrilateral in the complex plane.
It is an inscribed quadrilateral or cyclic quadrilateral.
It is simply a quadrilateral - there is no special name for such a quadrilateral.
It is an arrowhead quadrilateral
There is no specific name for such a quadrilateral.
No, a square is an equilateral quadrilateral. http://en.wikipedia.org/wiki/Quadrilateral