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