  Confocal quadrics lie at the heart of the system of confocal coordinates
(also called elliptic coordinates, after Jacobi). We suggest a discretization
which respects two crucial properties of confocal coordinates: separability and
all two-dimensional coordinate subnets being isothermic surfaces (that is,
allowing a conformal parametrization along curvature lines, or, equivalently,
supporting orthogonal Koenigs nets). Our construction is based on an integrable
discretization of the Euler-Poisson-Darboux equation and leads to discrete nets
with the separability property, with all two-dimensional subnets being Koenigs
nets, and with an additional novel discrete analog of the orthogonality
property. The coordinate functions of our discrete nets are given explicitly in
terms of gamma functions.
