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