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