  Given a triangulation of a closed topological cube, we show that (under some
technical condition) there is an essentially unique tiling of a rectangular
parallelepiped by cubes, indexed by the vertices of the triangulation.
Moreover, i - the combinatorics is preserved, and ii- the boundary is
preserved: vertices corresponding to the cubes at the corners of the
rectangular parallelepiped are at the corners of the topological cube. Also,
the sizes of the cubes are obtained as a solution of a variational problem
which is a discrete version of the notion of extremal length in three
dimensional Euclidean space.
