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