My favorite geometry is poorly defined geometry

A square is a regular polygon* with 4 sides.

*Regular Polygon A polygon which is both equiangular and equilateral (i.e. having all sides the same length and all interior angles the same).

Note that this doesn't preclude the existence of a square with curved sides if projected upon a sphere. But when discussing common geometry the assumption is that we are working within a single plane. If you wish to work in non-planar geometry, that must be explicitly called out in the diagram.