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circle
A circle is by definition 2-dimensional (flat). If you mean a circle that is wider in one direction than the other, than you are thinking of an ellipse.
Curved and flat faces.
In geometry, a circle is a two-dimensional object, so it does not have a surface. Only three-dimensional objects have surfaces. A disc is a flat, circular three-dimensional object.
There are zero diagonals in a circle because a circle has no sides no vertices or it doesn't have a flat surface so zero.