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