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A rhombus is first a polygon, then a quadrilateral, parallelogram, and finally a rhombus.
A rhombus may be a square or just a rhombus (a rhombus is merely called a rhombus when there are no 90 degree angles).
it has two names
Such a rhombus is not possible as it would not have all its sides equal. Or you can keep all angles right angles and call it a square.
A rhombus or a parallelogram is a 4 sided quadrilateral