  The last decade has seen applications of Adaptive Mesh Refinement (AMR)
methods for a wide range of problems from space physics to cosmology. With the
advent of these methods, in which space is discretized into a mesh of many
individual cubic elements, the contemporary analog of the extensively studied
line radiative transfer (RT) in a semi-infinite slab is that of RT in a cube.
In this study we provide an approximate solution of the RT equation, as well as
analytic expressions for the probability distribution functions (pdfs) of the
properties of photons emerging from a cube, and compare them with the
corresponding slab problem. These pdfs can be used to perform fast
resonant-line RT in optically thick AMR cells where, otherwise, it could take
unrealistically long times to transfer even a handful of photons.
