A cone
cone
The answer is a cone
It has [at least] one circular face and one curved face.
A conic section.
The solid that has one flat face, one curved face, one edge, and one vertex is a cone. The flat face is the circular base, the curved face is the conical surface, the edge is the circular boundary where the base meets the curved surface, and the vertex is the pointed tip of the cone.
cone
The answer is a cone
It has [at least] one circular face and one curved face.
A conic section.
pyramid
A cylinder.
A cone+++The original answer also had "Cube", which is obviously wrong!
The solid you are describing is called a cylinder. It has two circular faces, one curved face, and no vertices.
Cube and pyramid
Most don't, e.g. a cube or a sphere
A cone has one circular face. It also has one vertice. A cone has no edges due to the fact that it has a circular face.
A cone has one circular face. It also has one vertice. A cone has no edges due to the fact that it has a circular face.