Spheres
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A surface whose plane sections are all either ellipses or circles. A football approaches being an ellipsoid as does a discus.
Cylinder
2 objects are a race track and an egg. I know this because it was part of my science homework.
They are either kites or (if the diagonals bisect each other) rhombuses.
I think this is impossible the diagonals of a four sided figure will cross