[color=#999999]This activity belongs to the [i]GeoGebra book[/i] [url=https://www.geogebra.org/m/sw2cat9w]GeoGebra Principia[/url].[/color][br][br][br]A T-ellipsoid is the locus of points in space whose sum of T-distances to the foci is constant (k). It generally takes on the shape of a polyhedron with 18 rectangular faces and 8 triangular faces (which are E-regular but not T-regular).[br][br]The T-ellipsoid degenerates into an E-cuboctahedron when the absolute differences of the coordinates of the foci coincide; it degenerates into an E-cube when these differences also coincide with k; and it degenerates into a T-sphere (regular E-octahedron) when the foci coincide.[br][br]For certain special positions of the foci, a T-ellipsoid appears with all its faces formed by regular E-polygons, but it is neither a regular or semiregular E-polyhedron, as its vertices are not uniform.[br][br]Finally, when the T-distance between the foci is equal to k, we obtain an orthoedron.

[color=#999999]Author of the construction of GeoGebra: [url=https://www.geogebra.org/u/rafael]Rafael Losada[/url].[/color]