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