triangle
A cone would fit the given description
A right cylindrical cone has a circle for a base and one vertex. a diagram is shown on unitmath.com
L shape
The shape that is commonly known as a cone has two faces, one vertex and one edge. Mathematically, however, the cone has infinite height and so has one [curved] face and one vertex.
A cone has one vertex and one edge.
triangle
cone
How about a sphere as an example that fits the given description
A cone.
A cone would fit the given description
Conventionally, two faces, one edge and one vertex.
A cone would fit the given description.
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