regular polygon-all the sides are the same length and the angles have the same measurement.
polygon-a closed plane figure whose sides are segments that intersect at their endpoints.
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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.
If the octagon is a regular octagon (all eight sides and all eight angles are equal), then it is a regular polygon. If it is not a regular octagon (i.e. if it is an irregular octagon) then is it an irregular polygon.
From what I have been able to find out (using my daughter's homework) is that "Power Polygons" are any "normal" polygon that can be combined with another "normal" polygon to form another, different looking polygon (a mega-polygon, I guess?)that you can then divide up so you can see the individual "Power Polygon" pieces. Perhaps the name "Power Polygons" is derived from the fact that these polygons have the power to create other polygons. Logically then a "Power Polygon" is, really, just any polygon, just with a new, exciting, and high tech sounding name.
There is no such polygon.
For any polygon, there will be other shapes such that, together, they can tessellate.