A cone seems to fit the given description
a coneA cone.
edge
A cone.
The edge of a 3D shape is called an "edge." It is the line segment where two faces of the shape meet. In geometric terms, an edge is one of the fundamental components that define the structure of polyhedra and other solid figures.
An ellipsoid with a slice removed.
CONE
a coneA cone.
cylinder: 3 faces, 2 edges, no vertex
edge
None
All in the world a vertex is, is a corner (or where the edges meet) of any shape...not just 3d but of course it can be:)
A square based pyramid.
Cylinder
A cone.
The edge of a 3D shape is called an "edge." It is the line segment where two faces of the shape meet. In geometric terms, an edge is one of the fundamental components that define the structure of polyhedra and other solid figures.
It Is A Cone
An ellipsoid with a slice removed.