A cone has one vertex, one edge, and one base.
triangle
A cone would fit the given description
The solid shape you are describing is called a cone. A cone has a circular base and narrows to a single vertex, or apex, at the top. Its curved surface connects the base to the vertex, distinguishing it from other solid shapes.
A right cylindrical cone has a circle for a base and one vertex. a diagram is shown on unitmath.com
L shape
A cone has one vertex and one edge.
triangle
cone
How about a sphere as an example that fits the given description
A shape with one vertex, one edge, and two faces is called a cone. The vertex is the point where the edges meet, the edge is the line where the faces meet, and the faces are the flat surfaces of the shape. In the case of a cone, one face is the circular base and the other face is the curved surface.
A cone.
A cone would fit the given description
Conventionally, two faces, one edge and one vertex.
A right truncated cone.
It's a pentagonal pyramid.
A cone. It has 1 point, edge and 2 faces.
A right cylindrical cone has a circle for a base and one vertex. a diagram is shown on unitmath.com