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[[File:homoeoid3d.jpg|thumb|Homoeoid in 3D]]
A '''homoeoid''' is a shell bounded by two concentric, [[Similarity (geometry)|similar]] [[ellipse]]s (in 2D) or [[ellipsoid]]s (in 3D). 
When the thickness of the shell becomes negligible, it is called a '''thin homoeoid'''.

==Mathematical definition==
If the outer shell is given by

:<math>
\frac{x^2}{a^2}+\frac{y^2}{b^2}+\frac{z^2}{c^2}=1
</math>
with semiaxes <math>a,b,c</math> the inner shell is given for <math>0 \leq m \leq 1 </math> by

:<math>
\frac{x^2}{a^2}+\frac{y^2}{b^2}+\frac{z^2}{c^2}=m^2
</math>.

The '''thin homoeoid''' is then given by the limit
<math>
m \to 1
</math>

==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.

==References==
*[[Subrahmanyan Chandrasekhar|Chandrasekhar, S.]]: ''Ellipsoidal Figures of Equilibrium'', Yale Univ. Press. London (1969)
*[[Edward Routh|Routh, E. J.]]: ''A Treatise on Analytical Statics, Vol II'', Cambridge University Press, Cambridge (1882)

==See also==
*[[Focaloid]]

[[Category:Surfaces]]
[[Category:Mathematical physics]]
[[Category:Potentials]]