A circle could be considered to have "no sides" in theory, however under this definition it is not a polygon. Also, a circle could be considered to have infinite sides.
You could consider a point to be a no-sided polygon, but it's a stretch.
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A polygon with 6 sides is a hexagon and a polygon with 8 sides is an octagon
No the sides of a polygon can not cross
There is no formula for how many sides there are in a polygon; the name of the polygon shows how many sides it has.
A polygon with 3 sides is a triangle.
A polygon with 5 sides is a pentagon