Sphere

Sphere
Dimensions	2
Connected	Yes
Compact	Yes
Euler characteristic	2
Orientable	Yes
Genus	0
Symmetry	SO(3)

Ball
Rank	3
Space	Spherical
Notation
Tapertopic notation	3
Toratopic notation	(III)
Bracket notation	(III)
Elements
Faces	1 sphere
Measures (radius r)
Circumradius	$r$
Inradius	$r$
Volume	$\frac43\pi r^3$
Height	$2r$
Central density	1
Related polytopes
Dual	Ball
Conjugate	None
Abstract properties
Euler characteristic	1
Topological properties
Surface	Sphere
Orientable	Yes
Properties
Symmetry	O(3)
Convex	Yes
Nature	Tame

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.

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

• $x^2+y^2+z^2=r^2$

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.

External links

• Wikipedia Contributors. "Sphere".
• Hi.gher.Space Wiki Contributors. "Sphere".