The realization space is
  [1   1   0         1   0   1   1    0         1       1]
  [0   1   1   x1*x2^2   0   0   1    1   x1*x2^2      x2]
  [0   0   0         0   1   1   1   x1     x1*x2   x1*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[x2, x1*x2 - 1, x1, x1 - 1, x2 - 1, x1^2*x2^2 - x1*x2 - x1 + 1, x1*x2 + x2 - 1, x1*x2^2 - 1, x1*x2^2 - x2 - 1, x1*x2^2 + x1*x2 - 1, x1^2*x2^2 - x1 + 1, x1 + 1, x1^2*x2^2 + 1]