Various shapes do. The most obvious is a square, if you are looking for the 4 sides to be equal and the 4 angles to be equal. You can also have a rectangle or a parallelogram or a diamond shape and any arrangement of 4 sides for a shape.
More generally ,it is known as a quadrilateral (a polygon with four sides and four angles).
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4 sides and 4 interior angles
All quadrilaterals have 4 sides hence the root word quad. If you have 4 equal sides with 4 equal angles you have your basic square.
If all 4 sides are equal and the angles are not 90 degrees it is a rhombus.
A rhombus (4 congruent sides, diagonals perpendicular)that is not also a square (no right angles), andis also a parallelogram (opposite sides parallel and congruent, opposite angles congruent). It is also a quadrilateral, which has 4 sides.
A rhombus has 4 equal sides. Its angles can be right angles, but don't have to be. A square is a type of rhombus.