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