We describe a rich family of binary variables graphical models on planar graphs which
are equivalent to Gaussian Grassmann Graphical models (free fermions in statistical physics jargon). 
Calculation of partition function (weighted counting) in the models is easy (of polynomial complexity) 
as reduced to evaluation of determinants of matrixes linear in the number of variables. In particular,  
this family of models covers Holographic Algorithms of Valiant and extends on 
the Gauge Transformations discussed in our previous works.