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