2 parallel lines
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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.
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regular hexagons have 3 pairs of parallel edges
A square has 2 pairs of opposite parallel lines.
There cannot be parallel lines in any [plane] triangles.
A triangular prism has 9 parallel lines
there are 2 sets of parallel lines in a square