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