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A square a rectangle and a parallelagram or quadrilateral
No, rhombus refers to its shape, not the fact that is has four equal sides. You could call a rhombus an equilateral parallelogram by why would you want to? Also, would you then call a square a rhombic rectangle?
cube
parallel rectangle
Any shape that has 4 sides is a quadrilateral and some examples are:- square, rectangle, rhombus, parallelogram, trapezoid and a kite