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