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