yes
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Polygons can either be regular or irregular. A regular polygon is for example a octagon which has sides and angles that are all the same. Irregular they are not all the same.
No, equilateral and regular are the same thing.
In general no. A regular hexagon has the same length on all sides. Also, there are other hexagons with the same length on all sides that are not regular.
A regular octagon's angles and sides are all the same. As in the angles are the same, and the lengths of each side are the same. And irregular is basically the opposite of that.
Most polygons are not regular. A regular polygon is one in which all the sides are the same length AND all angle are the same measure. An irregular polygon is one for which either one or the other (or both) of these requirements are not met.