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