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