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