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