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.
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A square or rectangle has two sets of parallel lines. Stop signs technically have 4 short sets o parallel lines. Hexagon could have 3 sets, etc. All of which are polygons, though not all polygons have parallel lines.
2 parallel lines * * * * * The above answer is not wholly correct. A hexagon can have one, two or three pairs of parallel lines: a regular hexagon has 3 pairs.
2 parallel lines * * * * * The above answer is not wholly correct. A hexagon can have one, two or three pairs of parallel lines: a regular hexagon has 3 pairs.
In space with 3 or more dimensions, there are infinitely many pairs of lines that are not parallel and do not intersect.
Square, rectangle, rhombus