The realization space is
  [1   0   1                            x2   0   1    0             1                            x2                              x2    1]
  [0   1   1   -x1*x2 + x1 - 2*x2^2 + 2*x2   0   0    1             1   -x1*x2 + x1 - 2*x2^2 + 2*x2   -2*x1*x2 + x1 - 2*x2^2 + 3*x2   x1]
  [0   0   0                             0   1   1   -1   x1 + x2 - 1                          x2^2               x1*x2 + x2^2 - x2   x2]
in the multivariate polynomial ring in 2 variables over ZZ
within the vanishing set of the ideal
Ideal (x1^2 + 3*x1*x2 - 2*x1 + 2*x2^2 - 3*x2)
avoiding the zero loci of the polynomials
RingElem[x1 - 1, x1^2 + 2*x1*x2 - x1 - x2, x1, x1 + x2, x2, x2 - 1, x1 + x2 - 1, x1^2 + x1*x2 - x1 - x2^2 - x2, x1^2*x2 - x1^2 + 2*x1*x2^2 - 2*x1*x2 + x1 - x2^2 + x2, x1 + 2*x2, x1^2 + 2*x1*x2 - x1 + x2^2 - 2*x2, x1 + x2 - 2, x1^3 + 3*x1^2*x2 - 2*x1^2 + 2*x1*x2^2 - 5*x1*x2 + x1 - x2^2 + 2*x2, x1 + 2*x2 - 1, x1^3 + 3*x1^2*x2 - 3*x1^2 + 2*x1*x2^2 - 6*x1*x2 + 2*x1 - x2^2 + 3*x2]