The realization space is
  [1   0   1                           x1   0   1    0   x1^2 + x1*x2 - x1 - x2 + 1                           x1           x1^2 + x1*x2 - x1 - x2 + 1    1]
  [0   1   1   x1^2 + x1*x2 - x1 - x2 + 1   0   0    1   x1^2 + x1*x2 - x1 - x2 + 1   x1^2 + x1*x2 - x1 - x2 + 1   x1^3 + x1^2*x2 - x1^2 - x1*x2 + x1   x1]
  [0   0   0                            0   1   1   -1            x1^2 + x1*x2 - x1                  x1 + x2 - 1                    x1^2 + x1*x2 - x1   x2]
in the multivariate polynomial ring in 2 variables over ZZ
avoiding the zero loci of the polynomials
RingElem[x1 - 1, x1 + x2, x2 - 1, x1, x1 + x2 - 1, x1^2 - x2^2 + x2, x1^2*x2 + x1*x2^2 - 2*x1*x2 + x1 - x2^2 + x2, x1*x2 - x2 + 1, x2, x1^2 + x1*x2 - x1 - x2 + 1, x1^3 + x1^2*x2 - x1^2 - x1*x2 + x1 + x2 - 1, x1^3*x2 - 2*x1^3 + x1^2*x2^2 - 4*x1^2*x2 + 3*x1^2 - 2*x1*x2^2 + 4*x1*x2 - 2*x1 + x2^2 - 2*x2 + 1, x1^2 + x2 - 1, 2*x1^2 + 2*x1*x2 - 2*x1 - x2 + 1, x1^3 + x1^2*x2 - 3*x1^2 - 2*x1*x2 + 2*x1 + x2 - 1]