A cone does not have faces, edges or corners. A cone is defined as a hollow or solid object with a circular base that tapers upward to a point.
Faces are always flat, and a cone lacks any flat surfaces. Edges are always straight in their design and appearance. Edges exist through the formation of two faces. Because cones lack faces, it is impossible for them to have edges. In a similar vein, corners are formed when flat surfaces intersect at what essentially is a point. Again, because a cone lacks flat surfaces, they also lack corners. Although a cone does taper upwards to a point, that point is not formed by flat surfaces and thus does not constitute a corner.