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