Sphere

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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
Measures (radius r)
Circumradius
Inradius
Volume
Height
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[edit | edit source]

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

where r is the radius of the sphere.

Special properties[edit | edit source]

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[edit | edit source]