# Sphere

Sphere
Dimensions2
ConnectedYes
CompactYes
Euler characteristic2
OrientableYes
Genus0
SymmetrySO(3)
Local curvatureSpherical
Ball
Rank3
Notation
Tapertopic notation3
Toratopic notation(III)
Bracket notation(III)
Elements
Faces1 sphere
Circumradius${\displaystyle r}$
Inradius${\displaystyle r}$
Volume${\displaystyle {\frac {4}{3}}\pi r^{3}}$
Height${\displaystyle 2r}$
Central density1
Related polytopes
DualBall
ConjugateNone
Abstract & topological properties
Euler characteristic1
SurfaceSphere
OrientableYes
Genus0
Properties
SymmetryO(3)
ConvexYes

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.

## Coordinates

The points on a sphere are every point (x,y,z) such that

• ${\displaystyle x^{2}+y^{2}+z^{2}=r^{2}}$

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.
• Any section of a sphere will form a circle. Sections through the center of the sphere are known as great circles.