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