A polygon, polytope, or polyhedron’s vertex is its corner; it occurs when an object’s faces, facets, or edges meet; a sphere, however, lacks meeting points, hence it lacks vertices. A sphere has a single continuous surface, but because there are no points where it meets any other surface, there are no faces. Since spheres lack lines, they also lack edges.

Spheres differ from all other three-dimensional objects that students study in geometry in a few peculiar ways. It is not a polyhedron and by definition, it always possesses perfect symmetry (because it has no faces). Every surface point on a sphere is located exactly the same distance from the centre.

For a given surface area, spheres may hold the largest volume of any three-dimensional shape. This means that, for instance, the sphere has higher volume when comparing a pyramid and a sphere with the same values for surface area. One can pick up a balloon and begin inflating it to demonstrate this in action. Any form can be achieved due to the material’s flexibility, but a sphere (or at the very least, a spheroid) is the most effective because it holds the most air.