  The paper is concerned with interacting particle systems on the simple cubic
lattice obeying the nearest neighbour exclusion (NNE). This constraint forbids
any two neighbouring sites of the lattice to be simultaneously occupied, thus
reducing the set of admissible configurations for the cubic cell and its
subclusters such as edges and faces. This reduction extends applicability of
Kikuchi's Cluster Variation Method (CVM) with higher-order clusters to systems
with complex site configurations and short-range ordering, which would be
impractical beyond the NNE framework because of the "curse of dimensionality".
For edges of the cubic cell, which are the operational clusters of the
Bethe-Peierls entropy approximation in the CVM hierarchy, the edge-to-site
reduction of the entropy cumulants was studied previously. In extending the
earlier results, we develop a face-to-diagonal reduction of the Kramers-Wannier
entropy approximation of the CVM in the NNE setting. We also outline an
application of the resulting approximation to thermodynamic modeling of
disordered condensed media, such as liquid silicates, and discuss combinatorial
and numerical aspects of the implementation of this approach.
