Sphere

A sphere, formally known as a 2-sphere, is the set of all points in 3D space that are a certain distance away from a given point. This distance is known as the radius. While a sphere can be thought of as a limit polyhedron with infinitely many faces, spheres themselves are not considered to be polyhedra.

It is the higher-dimensional analogue of the circle.

Formally, a filled-in sphere is called a ball (specifically a 3-ball), and its boundary is called a sphere.

Vertex Coordinates
If a sphere is considered to be made of up infinitely many faces, then the vertices of a sphere are every point [x,y,z] such that

x2 + y2 + z2 = r2

where r is the radius of the sphere.

Special Properties
Spheres have many unique properties among the 3D shapes. These include:


 * They are rotationally symmetric from every angle.
 * They have the lowest surface-to-volume ratio of any closed 3D shape.
 * They have a constant width.
 * Any section of a sphere will form a circle. Sections through the center of the sphere are known as great circles.