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There are a few simple shapes with equal sides. The basic shapes are a square, octagon, and an equilateral triangle,
Shapes having less than 4 sides or more than 4 sides are not parallelograms
Both are quadrilaterals. A rectangle has 4 right angles, a rhombus has 2 pairs of equal angles (at opposite corners) A rhombus has 4 equal sides, a rectangle has 2 pairs of equal sides. The opposite sides in both shapes are parallel to each other.
not really a square and a diamond does
There is no special name. The term irregular is not appropriate because a rhombus is irregular but it has equal sides.