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