A rhombus and its variant (a square).
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No, a square is an equilateral quadrilateral. http://en.wikipedia.org/wiki/Quadrilateral
An equilateral quadrilateral is a rhombus (plural rhombi).
square
rhombus
A square has four sides so it is a quadrilateral. All sides of a square are of equal length so it is equilateral. All angles of a square are of equal measure so it is equiangular. A quadrilateral that is equilateral and equiangular is a regular quadrilateral.