Yes. A triangle is a type of polygon and it has NO parallel sides!!!!!!!
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Infinitely many. Polygons with 6 or more sides can have 3 pairs of parallel lines. Polygons with 7 or more sides can have a set of three parallel lines.
Any polygon with 4 or more sides can have 2 parallel sides.
Any regular polygon with an even number of sides must have parallel sides.
Squares and rectangles
Quadrilaterals. Parallelograms have two pairs of parallel sides.