There are many polygons that are both equiangular and equilateral. For example, squares and equilateral triangles are both equiangular and equilateral polygons. The general term for polygons that are both equiangular and equilateral is regular.
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A regular polygon
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A rhombus if i remember my geometry its a rhombus A rhombus is NOT equiangular. A square is the only quadrilateral with equal sides and equal angles. An equilateral triangle is also equiangular. Polygons that are equilateral and equiangular are called regular.
The polygon, as described in the question, is an equilateral polygon. If, in addition to this, all its angles have the same measure then the polygon is said to be regular. Polygons can be equilateral or equiangular or both (regular). The one exception is a triangle where equilateral implies (and is implied by) equiangular.