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