The realization space is
  [0   1   1   0   0   1      x2 - 1            x2 - 1         x2 - 1       x2 - 1                    x1*x2 - x1]
  [1   0   1   1   0   1   x1*x2 - 1      x1*x2^2 - x2   x1*x2^2 - x2    x1*x2 - 1   x1*x2^2 + x1*x2 - x1 - x2^2]
  [1   0   1   0   1   0      x2 - 1   x1*x2^2 - x1*x2      x2^2 - x2   x1*x2 - x1               x1*x2^2 - x1*x2]
in the multivariate polynomial ring in 2 variables over ZZ
avoiding the zero loci of the polynomials
RingElem[x1 - x2, x2 - 1, x2, x1 - 1, x1^2*x2^2 - x1*x2^2 - 2*x1*x2 + x1 + x2^2, x1^2*x2 - 3*x1*x2 + x1 + x2^2, x1^2*x2^2 - x1*x2^3 + x1*x2^2 - 3*x1*x2 + x1 + x2^2, x1*x2 - 1, x1*x2^2 + x1*x2 - x1 - x2^2, 2*x1*x2 - x1 - x2^2, x2 + 1, x1*x2^2 - x2^2 - x2 + 1, x1, x1*x2^2 - 2*x2 + 1, x1*x2 - 2*x2 + 1]