Answer:
Depending on what information and grade level the following would be considered for a three dimensional cone:
If the definition of a face= a flat side
edge= where to faces meet
vertex= where three or more faces meet
then cone would have 1 face (the base), 0 edges, 0 vertices
If the curriculum includes curved surfaces as faces then:
cone would have 2 faces, 1 edge, 0 vertices
The above was using a 4th grade Macmillan McGraw-Hill Oklahoma textbook copyright 2011.