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A square is a regular quadrilateral.

That is, a regular polygon with $4$ sides.

That is, a square is a plane figure with four sides all the same length and whose angles are all equal.


Also see

Euclid's Definition

In the words of Euclid:

Of quadrilateral figures, a square is that which is both equilateral and right-angled; an oblong that which is right-angled but not equilateral; a rhombus that which is equilateral but not right-angled; and a rhomboid that which has its opposite sides equal to one another but is neither equilateral nor right-angled. And let quadrilaterals other than these be called trapezia.

(The Elements: Book $\text{I}$: Definition $22$)