The realization space is
  [1   0   1       1   0   1    0         x1       1    1         x1]
  [0   1   1   x1*x2   0   0    1         x1   x1*x2   x2      x1*x2]
  [0   0   0       0   1   1   -1   2*x1 - 1      x1    1   2*x1 - 1]
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 - 1, x2 - 1, x1, x1*x2 + x1 - 1, 2*x1 - 1, x1*x2 + 2*x1 - 1, x1^2*x2 - x1*x2 - 2*x1 + 1, x1*x2 - 1, x2 + 1, 2*x1*x2 - x1 - x2, x1^2*x2 - 3*x1*x2 + x1 + x2, x1*x2 - 2*x1 + 1, x1*x2 - x2 - 1, x1^2*x2 + x1^2 - 3*x1 + 1, 3*x1 - 1, x1^2*x2 - 3*x1 + 1, x1*x2 - x2 + 1]