It could be a cylinder or a cuboid
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There are several cases: any 3 dimensional or more object. Since a polygon is defined as being confined to a single plane, any shape that violates the plane is not a polygon but may still have parallel bases. For cases in only 2 dimensions: Any object that has curves in addition to the parallel bases. A polygon's definition includes only straight sides. Finally, unclosed shapes can have 2 parallel bases with out being polygons even if in a single plane and made up of only straight line sides. A polygon must be closed.
No but a cylinder does have 2 parallel bases
Yes, every prism has 2 parallel bases.
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Any polygon with 4 or more sides can have 2 parallel sides.