Naming quadrilaterals Is there a rule for naming quadrilaterals in English? What I am expected to know about are: square, rhombus, rectangle, parallelogram, trapezium, kite. But how do we name other quadrilaterals?
 A: You've left out at least one named type of quadrilateral, the cyclic quadrilateral. See here for information. Many more are named here, including quite a few I have never heard of.  
A: There is also a diamond, which is a square rotated through 45$^\circ$, but again, the nomenclature here obscures as much as it reveals. As other posters have pointed out "quadrilateral" captures the essential properties of the object well enough that a more specific taxonomy would be unhelpful.
A: 
i am looking for rule to name any quadrilateral

This is inherently vague, but we can add a few points I guess.
First of all, I'm working under the impression that you understand the "hierarchy of quadrilaterals," and that you believe they are organized by their properties and not by rules established arbitrarily by gradeschool teachers. That being the case, you see squares are rectangles are parallelograms etc.
If that's the case, then the only types of quadrilaterals that don't fall under one of the categories you mentioned are things that aren't kites, and aren't trapezoids, since those are the biggest classes of the quadrilaterals you named. Such quadrilaterals don't have any parallel sides, and have at least three different side-lengths, so there isn't really a lot you can say about them. (Perhaps "has a pair of congruent opposite angles" or "has a pair of congruent adjacent angles" maybe.
