  The 3d Ising model on a regular cubic lattice can be expressed in terms of an
SU(2) 2d fermionic model with a $Z_2$-fluxes. We modify the model such that it
is defined on the dual to a body centered cubic lattice. The advantage of this
lattice is that 2d embedded surfaces have no selfintersections, thus partially
avoiding the Sign-factor problem associated with the 2d fermionoc models
related to the 3d Ising model. Rather than solving the full SU(2) fermionic
theory on this lattice we study the simpler model of scalar fermions and find
the spectrum of excitations. The model has no mass gap. We reformulate the
model using the R-formalism and a new interesting structure appears due to the
necessity of introducing a three-paticle matrix $R^{(3)}_{ijk}$. It encodes the
essential character of the Sign-factor. We analyse the integrability properties
of this class of models.
