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A hexagon or any of a selection of polyhedrons with 10 or more sides. I am not sure that less than 10 sides will suffice but they may well do.

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Q: What polygon has exactaly three parallel SIDES?
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What is a polygon with 3 parallel lines?

There can be no convex polygon with three parallel sides. There are concave polygons with 6 or more sides that have three parallel lines.


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A 4-sided polygon with four or three sides of different lengths can readily be constructed so that no two sides are parallel. The shapes so obtained will not have an axis of symmetry. However, a kite is a quadrilateral having two pairs of adjacent sides of equal length but does not have any parallel sides. It is symmetrical about its long axis.


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