No, this is impossible as 'parallel' relates more than one object at a time.
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A HEXAGON. Opposite sides of a regular hexagon are parallel. There being three sets set at different angles.
It is possible for a hexagon to have one pair of parallel sides. A hexagon can have 0, 1, 2 or 3 pairs of parallel sides, and can have 0, 2, 3, 4, 5, or 6 parallel sides.
a hexagon
Most hexagons have no parallel lines. A regular hexagon has 3 sets of parallel lines. A hexagon can have 0, 2, 3, 4, 5, or 6 parallel lines.
It is possible but not necessary for a hexagon to have 3 pairs of parallel sides. In particular, a regular hexagon has 3 pairs of parallel sides.