  F-boxes defined in [6] as hyper-boxes in N^{\infty} discrete space were
applied here for the geometric description of the cobweb posetes Hasse diagrams
tilings. The F-boxes edges sizes are taken to be values of terms of natural
numbers' valued sequence F. The problem of partitions of hyper-boxes
represented by graphs into blocks of special form is considered and these are
to be called F-tilings. The proof of such tilings' existence for certain
sub-family of admissible sequences F is delivered. The family of F-tilings
which we consider here includes among others F = Natural numbers, Fibonacci
numbers, Gaussian integers with their corresponding F-nomial (Binomial,
Fibonomial, Gaussian) coefficients. Extension of this tiling problem onto the
general case multi F-nomial coefficients is here proposed. Reformulation of the
present cobweb tiling problem into a clique problem of a graph specially
invented for that purpose - is proposed here too. To this end we illustrate the
area of our reconnaissance by means of the Venn type map of various cobweb
sequences families.
