Click on the image below to view it full size in an image viewer !
Convex quadrilaterals are further classified as follows:

While this apparent domain class explosion is necessary for the domain taxonomy, it does not follow that one should have an implementation class for every type of quadrilateral. The vertex Points are in general time (or parameter) dependent, so one can imagine a quadrilateral switching between forms during one lifetime.

One aims to encapsulate the variation in interfaces through parametrisation of the implementation as much as possible. Also, using port-based engineering, dedicated interfaces can be dynamically and lazily allocated as and when conditions are met.

So, did you suspect that there is so much to a square ? Often there is more to a taxonomy than meets the eye. Thanks Wikipedia !

This diagram is already beyond the classic 7+/-2 rule of graphical complexity, so let's now break it down, using of course the focus diagrams for each «wrapper» Component ..

Notes

Note imitation of a source document diagram with UML model elements in a UML diagram (only approximate)