If the outer shell is given by

${\displaystyle {\frac {x^{2}}{a^{2}}}+{\frac {y^{2}}{b^{2}}}+{\frac {z^{2}}{c^{2}}}=1}$ 

with semiaxes ${\displaystyle a,b,c}$  the inner shell is given for ${\displaystyle 0\leq m\leq 1}$  by

${\displaystyle {\frac {x^{2}}{a^{2}}}+{\frac {y^{2}}{b^{2}}}+{\frac {z^{2}}{c^{2}}}=m^{2}}$ .

The thin homoeoid is then given by the limit ${\displaystyle m\to 1}$ 

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]

• Focaloid

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