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One: the flat base.
1 because all of the shape is curved except for the flat surface on the bottom
2 faces (around the curved part and the flat base) 1 vertex (the point at the top) 1 edge (where the curved section meets the flat base)
2 faces
Mathematically, a cone is infinite and so has no flat surface. The popular cone is actually a truncated cone and does have 1 flat surface.