  The Falicov-Kimball model of spinless quantum electrons hopping on a
1-dimensional lattice and of immobile classical ions occupying some lattice
sites, with only intrasite coupling between those particles, have been studied
at zero temperature by means of well-controlled numerical procedures. For
selected values of the unique coupling parameter $U$ the restricted phase
diagrams (based on all the periodic configurations of localized particles
(ions) with period not greater than 16 lattice constants, typically) have been
constructed in the grand-canonical ensemble. Then these diagrams have been
translated into the canonical ensemble. Compared to the diagrams obtained in
other studies our ones contain more details, in particular they give better
insight into the way the mixtures of periodic phases are formed. Our study has
revealed several families of new characteristic phases like the generalized
most homogeneous and the generalized crenel phases, a first example of a
structural phase transition and a tendency to build up an additional symmetry
-- the hole-particle symmetry with respect to the ions (electrons) only, as $U$
decreases.
