It sounds as though you are describing a rhombus, which is a parallelogram in which all sides are equal.
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A shape with four equal sides and no right angles is called a rhombus. A rhombus is a type of quadrilateral where all four sides are of equal length, but the angles are not 90 degrees. The opposite angles of a rhombus are equal to each other, making it a special type of parallelogram.
Rectangle
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.
This is a parallelogram called a rectangle. A square has four right angles and four sides that are equal in length.
A shape that has 2 pairs of equal sides and no right angles is a kite or a parallelogram. In a parallelogram, each side is equal to the one directly opposite; in a kite, the equal sides are adjacent to one another.
Rhombus