How to denote square uniquely in Euclidean $\mathbb{R}^2$?

Question

I am eager to know how one can denote a square in the $\mathbb{R}^2$ Euclidean space. I mean I can write as $[\text{centre of square}, \text{dimension}]$ but how would I know its orientation then. Is there way used in literature to define a square?

Also is there a literature addressing the general polygon shapes as well.