The realization space is
  [1   1   0    1   0   1   1                        0        x1 - x2                   x2 - 1         x1 - 1]
  [1   0   1   x1   0   1   0   x1^2 - x1*x2 - x1 + x2   x1^2 - x1*x2   x1^2 - x1*x2 - x1 + x2   x1^2 - x1*x2]
  [0   0   0    0   1   1   1               x1*x2 - x1     x1*x2 - x2               x1*x2 - x1     x1*x2 - x2]
in the multivariate polynomial ring in 2 variables over ZZ
avoiding the zero loci of the polynomials
RingElem[x1^2 - x1*x2 - x1 + 1, x1 - x2, x1^2 - 2*x1*x2 + x2, x1^2*x2 - 3*x1*x2 + x1 + x2, x1, x2 - 1, x2, x1^3 - 2*x1^2*x2 - x1^2 + 2*x1*x2^2 + x1 - x2^2, x1^3*x2 - 4*x1^2*x2 + x1^2 + 2*x1*x2^2 + x1*x2 - x2^2, 2*x1 - 1, x1^2 - x1 - x2 + 1, x1*x2 - 2*x2 + 1, x1 - 1, x1^2 - 2*x1 + x2, x1^2*x2 - x1*x2 - x1 + x2]