A homoeoid is a shell (a bounded region) bounded by two
concentric,
similarellipses (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]