  Cubic blocks are studied assembled from linear operators $\mathcal R$ acting
in the tensor product of $d$ linear "spin" spaces. Such operator is associated
with a linear transformation $A$ in a vector space over a field $F$ of a finite
characteristic $p$, like "permutation-type" operators studied by Hietarinta.
One small difference is that we do not require $A$ and, consequently, $\mathcal
R$ to be invertible; more importantly, no relations on $\mathcal R$ are
required of the type of Yang--Baxter or its higher analogues.
  It is shown that, in $d=3$ dimensions, a $p^n\times p^n\times p^n$ block
decomposes into the tensor product of operators similar to the initial
$\mathcal R$. One generalization of this involves commutative algebras over $F$
and allows to obtain, in particular, results about spin configurations
determined by a four-dimensional $\mathcal R$. Another generalization deals
with introducing Boltzmann weights for spin configurations; it turns out that
there exists a non-trivial self-similarity involving Boltzmann weights as well.
