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It has two 5-tuples and 5 pairs of parallel lines. It need not have any line of symmetry.
A parallelogram, or selected irregular polygons with 5 or more sides
Pentagon
It can have none, one (1 pair), two (2 pairs), 3 (one triplet), 4 (two pairs), 5 (one pair + one triplet) or 6 (three pairs or two triplets) of parallel lines.
There are parallel lines, rectangles and arrays of stars 5 by 6 and 4 by 5.