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