How Many Vertices Does a Sphere Have?

woodleywonderworks/CC-BY 2.0

A vertex is a corner on a polygon, polytope or polyhedron, and when faces, facets or edges of an object come together, a vertex forms; however, because a sphere features no meeting points, it has no vertices. Even though a sphere does have one continuous surface, its lack of meeting points with any other surface means that it technically has no faces. Spheres have no lines, so they also have no edges.

Spheres have some oddities that make them different from all other three-dimensional objects that students learn about in geometry. It always has perfect symmetry, by definition, and it is not a polyhedron (because it has no faces). On any sphere, all of the surface points are precisely the same distance from the middle.

Among all of the three-dimensional shapes, spheres can contain the most volume for a set surface area. This means that when comparing a pyramid and sphere with identical surface area values, for example, the sphere has more volume. To see proof of this in action, an individual can pick up a balloon and start inflating it. The flexible material allows it to take any shape, but the most efficient is a sphere (or at least a spheroid) because that holds more air than any other shape.