A square, pentagon, decagon, octagon are always regular polygons.
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Yes, a regular polygon is always equiangular.
Squares, rhombera, and equilateral triangles are always regular.
Not always
The term regular polygon is almost always used to refer to a polygon that has equal interior angles and equal side lengths. In that light, the equiangular polygon and a regular polygon are the same thing.
A regular polygon.