This question is very difficult to answer because of the ambiguity of what an "arrow" is. An arrow that you might fire from a bow is a three dimensional object and so is not a polygon. An arrow drawn as a straight line with a direction indicator at its head with or without tail feathers (for example <|----<< : oh, the graphics on this browser are so good, aren't they!) is not a polygon because the shaft is a line: a 1-dimensional object. An arrow such as the default one used to represent the cursor in Windows is a concave heptagon.
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an arrow is or isn't a polygon?
An arrow can be a polygon. A polygon is any two dimensional plane figure. An arrow can, obviously, be a three dimensional object.
A polygon is a shape that is closed with straight sides and the sides do not overlap like these. I don't know if an arrow is a polygon.
An arrow head has 4 sides and it is a quadrilateral polygon
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