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