---
tag: MRC4WMVTAH
kind: concept
name: Circumsphere
msc: [51M04, 51M20]
sources:
  - url: https://en.wikipedia.org/wiki/Circumscribed_sphere
same_as:
  wikidata: Q1414689
  wikipedia: Circumscribed sphere
---

## Summary

The circumsphere of a [[simplex|YX1DJK2QAG]] is the unique [[sphere|P9CM4GQ2T0]] in its affine span that passes through all its vertices.
Its centre is the circumcentre and its radius the circumradius.
For a triangle it is the [[circumcircle|03VZJE6C8C]], and for a [[tetrahedron|JFX8ASQS3E]] it is a sphere through the four vertices.
The word is also used for a sphere through all vertices of a polyhedron, which exists only for some polyhedra.

## Explanations

### L1 human

Through any three points that are not on a line there is exactly one circle.
In space, through any four points not in a plane there is exactly one sphere.
That sphere is the circumsphere of the tetrahedron with these four corners.
For the cube with corners $(\pm 1, \pm 1, \pm 1)$, the sphere of radius $\sqrt{3}$ about the origin passes through all eight corners.