One edge (boundary) and no vertices.
one
A cone.
A cone has only one edge simply because it only has one face. Although one face may have several edges, a circle is a closed figure with only one vertice, resulting in one edge. The rest of the shape is 3-D, but with only one face, there is an infinite amount of points on a cone. The cone joins on another vertice, but since the face is a circle, there is still only one actual edge. Thus, there is only one edge on a cone because there is a single, circular face.
A cone would fit the given description
Well it has one edge, one face, one base(the face that the shape sits on), and one vertice.
One edge (boundary) and no vertices.
If a cylinder has two edges then a cone by that definition has one edge and one vertice.
one
A cone.
Conventionally, two faces, one edge and one vertex.
A cone has only one edge simply because it only has one face. Although one face may have several edges, a circle is a closed figure with only one vertice, resulting in one edge. The rest of the shape is 3-D, but with only one face, there is an infinite amount of points on a cone. The cone joins on another vertice, but since the face is a circle, there is still only one actual edge. Thus, there is only one edge on a cone because there is a single, circular face.
There is no such shape - unless there are other faces. If there is one rectangular face then you require at least four other faces - one on each edge of the rectangle - making a minimum of 5 faces.
Circle
A cone perhaps
It has one spherical face and no vertices or edges
A cone would fit the given description