No,
If all angles are equal and all sides are equal, then it is a regular polygon (otherwise it is 'irregular'). In this case, parallelogram is irregular.
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A 6 sided hexagon polygon can be regular or irregular.
as far as I know a polygon is anything with more than 3 sides. So technically yes.
Yes, a regular polygon has all sides of equal length. An irregular polygon is any polygon that is not regular.
what is a regular polygon
No. There can be no regular concave polygon.