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