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