An infinite number.
A shape can have an infinite number of sides - half of these numbers will be even and half odd. Half of infinity is still infinity.
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Try counting the sides.
An hexagon has 6 sides
5 Shapes, 8 sides
polygon
Infinitely many. Every regular polygon with 2n sides has n pairs of parallel sides. Then there are irregular polygons which can have parallel sides. And there are also irregular shapes which have parallel sides.