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A parallelogram is a four sided shape where opposite sides are parallel and equal lengths. If you mean that ALL sides are equal lengths, you are looking for a rhombus.
A rhombus is a shape having two acute angles and four equal sides.
A "parallelogram" technically is a shape where opposite sides are equal and any shape with four sides is a "quadrilateral". Every square has four sides of equal length, so a square is both a parallelogram and a quadrilateral. A rhombus(or diamond shape) can have four sides of equal length and can be a parallelogram as well, so either are possibilities.
The rectangle
A square is a two-dimensional shape with four equal sides and four right angles.