# Sphere

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Sphere | |
---|---|

Dimensions | 2 |

Connected | Yes |

Compact | Yes |

Euler characteristic | 2 |

Orientable | Yes |

Genus | 0 |

Symmetry | SO(3) |

Local curvature | Spherical |

Ball | |
---|---|

Rank | 3 |

Notation | |

Tapertopic notation | 3 |

Toratopic notation | (III) |

Bracket notation | (III) |

Elements | |

Faces | 1 sphere |

Measures (radius r) | |

Circumradius | |

Inradius | |

Volume | |

Height | |

Central density | 1 |

Related polytopes | |

Dual | Ball |

Conjugate | None |

Abstract & topological properties | |

Euler characteristic | 1 |

Surface | Sphere |

Orientable | Yes |

Genus | 0 |

Properties | |

Symmetry | O(3) |

Convex | Yes |

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.