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 polyhedron with infinite faces, spheres themselves are not considered to be polyhedrons.

It is the higher-dimensional analogue of the circle.

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

x2 + y2 + z2 = r2

where r is the radius of the circle.

Special Properties
Spheres have many unique properties among the 2D shapes. These include:


 * They are rotationally symmetric from every angle.
 * They have the lowest surface-to-volume ratio of any closed 3D shape. This is why gravity shapes celestial bodies into roughly spherical shapes (due to rotation, most celestial bodies are slightly oblate rather than being perfect spheres).
 * They have a constant width.
 * Any section of a sphere will form a circle. These are known as great circles.