The tip of the cone.
a cone
A cone.
a cone
A cone !
2
In 2-D: circles, ellipses, smooth loops or in 3-D spheres, ellipsoids, smoothed blobs have none. A cone has only one vertex.
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).
A normal cone has a circular face as its base, and a slanting surface which goes from the circumference of this face to the vertex. So it has two faces. Mathematicians also refer to the infinite equivalent as a cone. This could be considered as a 3-d shape with one face.
A vertex of a 3-d object, such as a star, where 6 faces meet.
A 3-D cone would act as the ice cream cone and a 3-D sphere would act as the ball of ice cream.
a truncated cone
A cone