The realization space is
  [1   0   1   1   3*x1 - 2   x1 - 1   0   x1 - 1                                  0   x1 - 1    1]
  [0   1   1   1     x1 - 1      -x1   0        0                    x1^2 - 2*x1 + 1      -x1   x1]
  [0   0   0   1     x1 - 1   x1 - 1   1      -x2   x1^2 + 3*x1*x2 - 2*x1 - 2*x2 + 1      -x2   x2]
in the multivariate polynomial ring in 2 variables over ZZ
avoiding the zero loci of the polynomials
RingElem[x1, x2, x1 - x2, x1 + x2 - 1, x1^3 + 2*x1^2*x2 - 2*x1^2 + x1 - x2, x1^2 + 3*x1*x2 - 2*x1 - 2*x2 + 1, x1^2 + 2*x1*x2 - 2*x1 - x2 + 1, x1^2 + 2*x1*x2 - x1 - x2, x1^2 + x1 - 1, x1 - 1, 3*x1^2 - 3*x1 + 1, x2 - 1, 2*x1 - 1, 3*x1*x2 - x1 - 2*x2 + 1, 2*x1^3 + 5*x1^2*x2 - 5*x1^2 - 5*x1*x2 + 4*x1 + x2 - 1, x1^3 + 5*x1^2*x2 - 2*x1^2 - 5*x1*x2 + x1 + x2, 2*x1^3 + 3*x1^2*x2 - 5*x1^2 - 2*x1*x2 + 4*x1 - 1, 3*x1 - 2]