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?
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A square is also a rectangle, a rhombus, a parallelogram, and a quadrilateral.
Six names that you can call a square are rhombus, square, rectangle, kite, trapezoid, or parallelogram. All of these shapes have four corners and are known as quadrilaterals.
Parallelogram. You could also call it a rhombus if all sides are the same length, but a rhombus is technically a parallelogram.
A parallelogram with 4 equal sides is a rhombus
trapezoid, parallelogram, and rhombus (people call it the diamond)