A rhombus is a type of quadrilateral, which is a type of polygon.
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If every side of the polygon is the same length, then it is a regular polygon. If the measure of every internal angle of a polygon is the same as every other, then it is a regular polygon. The two always go together, so you need to check only one of the above criteria.
square and rhombus
Every polygon has two of its sides intersect.
Yes, it is!
No. A circle, for example, is a closed shape but it is not a polygon.