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