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