The realization space is
  [1   1   0   0   1   1                 0                      x1^3 - x1^2 + x1*x2           x1^2 - x1 + x2     x1^3 - x1^2 + x1*x2                x1^3 - x1^2 + x1*x2]
  [0   1   1   0   0   1                x2                            -x1*x2 + x2^2   x1^2 - x1*x2 - x1 + x2           -x1*x2 + x2^2   x1^2*x2 - x1*x2^2 - x1*x2 + x2^2]
  [0   0   0   1   1   1   -x1^2 + x1 - x2   x1^3 - x1^2*x2 - x1^2 + 2*x1*x2 - x2^2      x1^3 - x1^2 + x1*x2   x1^4 - x1^3 + x1^2*x2        x1^3*x2 - x1^2*x2 + x1*x2^2]
in the multivariate polynomial ring in 2 variables over ZZ
avoiding the zero loci of the polynomials
RingElem[x1^2 - x1 + x2, x1 - 1, x2, x1 - x2, x1, x1^2 - 2*x1 + x2, x1^3 - x1^2*x2 - x1^2 + 3*x1*x2 - x2^2, x1^3 - 2*x1^2 + 2*x1*x2 + x1 - x2, x1^2*x2 - x1^2 + 2*x1*x2 - x2^2, x1*x2 - x1 + x2, x1^4*x2 - x1^4 + x1^3 + x1^2*x2^2 - 3*x1^2*x2 + 3*x1*x2^2 - x2^3, x1^3 - x1^2*x2 - x1^2 + x1*x2^2 + 2*x1*x2 - x2^2, x2 - 1, x1^3*x2 - x1^3 + x1^2 - 2*x1*x2 + x2^2, x1^3 - x1^2 + 2*x1*x2 - x2^2, x1^4 - x1^3 + x1^2*x2 + x1*x2 - x2^2, x1^4 - 2*x1^3 + x1^2*x2 + x1^2 - 2*x1*x2 + x2^2, x1^2 - x1 + 2*x2]