A quadrilateral with 4 equal sides and 4 right angles is a square.
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A rhombus, an equal sided parallelogram or an equal sided quadrilateral with no right angles.
The shape you are looking for is a quadrilateral. If you have a square, all angles MUST be right angles. A parallelogram can also have 4 equal sides in length and parallel sides, but a parallelogram doesn't have right angles.
A rectangle is a quadrilateral with four sides. All angles are right angles, the diagonals are congruent, and the opposite sides are all equal. A rhombus (diamond) is a quadrilateral with congruent daigonals and equal angles.
Every square is a regular quadrilateral because they have 4 equal sides and 4 equal right angles.
A rhombus.