rhombus, a "streched out" diamond
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Yes, trapezoid
A quadrilateral is a polygon with four sides. A rectangle is a quadrilateral
rectangle, rhombus, parallelogram, trapezoid, isosceles trapezoid, kite ... etc
A rectangle comes to mind. A rectangle is equiangular (all angles the same) and is also a quadrilateral (four-sided), but is not equilateral (all sides of the same length).
A rectangle is always a quadrilateral and a parallelogram.