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Why do polygons fit together to cover a flat surface?
Only when they tessellate.
Are the faces of a polyhedron all flat surfaces?
Yes and its flat surface faces are in regular shapes.
What is a flat closed surface that has congruent and parallel opposite sides?
That could be numerous polygons: a square, a regular hexagon, a regular octagon, a regular dodecagon ... Any regular polygon with an even number of sides could be your answer.
Why is the shape of a football not a polygon?
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.
How many polygons does a cone have?
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.
