cone
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One possible answer is an infinite cone. Spheres have one face but no vertex. No physical 3-D shape can have a vertex without having more than one face (a real cone typically has two: side and bottom).
Faces-2 (1 flat face and 1 curved face), 1 curved edge, and 1 vertex.
1 corner,0 vertices and 0 edges * * * * * A vertex is the same as a corner, so a cone has 1 vertex. It has two faces: one circular and one curved. It has one edge where the two faces meet.
sphere
A cone has 1 vertex, 1 circular edge and 2 faces