It is impossible to count the edges of a 3d anything. A cone is 3D anyway so it is impossible. Another reason it is impossible to count the edges is that a cone is made out of circles. If you drew a 2D cone, it wouldn't be a cone anymore, it would be a triangle. So, in essence, a cone is a tri-agnle which has three sides; but a cone is 3D and, as I said before, the edges cannot be counted on a 3D object.
2
The tip of the cone.
A 3-D cone would act as the ice cream cone and a 3-D sphere would act as the ball of ice cream.
The Euler characteristic for polyhedra then requires that thye shape has no vertices! And that means it cannot be a polyhedron. I suggest you count the faces and edges again.
One possible answer is an infinite cone. Spheres have one face but no vertex. No physical 3-D shape can have a vertex without having more than one face (a real cone typically has two: side and bottom).
a truncated cone
A cone.
A pentagonal pyramid has 10 edges.
there are 12 (twelve) edges.
A cone
a cone
A sphere