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