A **homoeoid** is a shell (a bounded region) bounded by two concentric, similar ellipses (in 2D) or ellipsoids (in 3D).^{[1]}^{[2]}
When the thickness of the shell becomes negligible, it is called a **thin homoeoid**. The name homoeoid was coined by Lord Kelvin and Peter Tait.^{[3]}

## Mathematical definition

If the outer shell is given by

with semiaxes the inner shell is given for by

- .

The **thin homoeoid** is then given by the limit

## Physical meaning

A homoeoid can be used as a construction element of a matter or charge distribution. The gravitational or electromagnetic potential of a homoeoid homogeneously filled with matter or charge is constant inside the shell. This means that a test mass or charge will not feel any force inside the shell.^{[4]}

## See also

## References

**^**Chandrasekhar, S.:*Ellipsoidal Figures of Equilibrium*, Yale Univ. Press. London (1969)**^**Routh, E. J.:*A Treatise on Analytical Statics, Vol II*, Cambridge University Press, Cambridge (1882)**^**Harry Bateman. "Partial differential equations of mathematical physics.", Cambridge, UK: Cambridge University Press, 1932 (1932).**^**Michel Chasles,*Solution nouvelle du problème de l’attraction d’un ellipsoïde hétérogène sur un point exterieur*, Jour. Liouville 5, 465–488 (1840)