  This paper provides explicit justification for a method of canonical scalings
of tilings of euclidean spaces. We present a new combinatorially-geometrical
approach for constructing a generatriss of a tiling. The approach is based on
an operation of lifting of a tile up to a lifted neighbour. We use this
approach and give a new short geometrical proof of a fundamental theorem of
theory of parallelotopes: Voronoi's Conjecture holds for a given parallelotope
$P$ if and only if the corresponding tiling $\mathcal T_P$ admits a canonical
scaling.
