Only when they tessellate.
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Triangles, squares and hexagons. That is if they all have to be the same. If you use different regular polygons, you can tile a flat surface with triangles and 12-sides or with squares and 8-sides for example.
A football has a curved surface and polygons are flat. You can approximate a curved surface quite well if you use enough polygons but each polygon will still be flat and a football does have a curved (and rough) surface. Using a few thousand polygons you can create an approximation of a football with stitching seams and every detail but you will not have a curved surface you will have an approximation of a curved surface.
None. A cone is a surface of revolution and thus it has no flat sides. Polygons are planar figures. A cone has no planar faces.
Yes and its flat surface faces are in regular shapes.
Flat shapes such as polygons are two-dimensional.