The realization space is
  [1   1   0   0   1   1                   0            -x1^4 + 3*x1^3*x2 - 3*x1^2*x2^2 - x1^2*x2 + x1*x2^3 + 2*x1*x2^2 - x2^3        x1^2 - x1*x2 + x2        x1^2 - x1*x2 + x2          x1^2 - x1*x2 + x2]
  [1   0   1   0   1   0                  x2   -x1^4 + 3*x1^3*x2 - 3*x1^2*x2^2 - 2*x1^2*x2 + x1*x2^3 + 4*x1*x2^2 - x2^3 - x2^2                    x1*x2                     x1^2                      x1*x2]
  [0   0   0   1   1   1   x1^2 - x1*x2 + x2                    -x1^4 + 3*x1^3*x2 - 2*x1^2*x2^2 - 2*x1^2*x2 + 3*x1*x2^2 - x2^2   x1^3 - x1^2*x2 + x1*x2   x1^3 - x1^2*x2 + x1*x2   x1^2*x2 - x1*x2^2 + x2^2]
in the multivariate polynomial ring in 2 variables over ZZ
avoiding the zero loci of the polynomials
RingElem[x1 - x2, x1, x2, x1 - 1, x1^2 - 2*x1*x2 + x2^2 + x2, x2 - 1, x1^2 - 2*x1*x2 + x2, x1 - x2 + 1, x1^2*x2 - x1^2 - x1*x2^2 + 2*x1*x2 + x2^2 - x2, x1^3 - 2*x1^2*x2 - x1^2 + x1*x2^2 + 2*x1*x2 - x2, x1^3 - 2*x1^2*x2 - 2*x1^2 + x1*x2^2 + 4*x1*x2 - x2^2 - x2, x1^5 - 3*x1^4*x2 - x1^4 + 3*x1^3*x2^2 + 5*x1^3*x2 - x1^2*x2^3 - 6*x1^2*x2^2 - 3*x1^2*x2 + 2*x1*x2^3 + 5*x1*x2^2 - x2^3 - x2^2, x1^2 - x1*x2 + x2, x1^3 - x1^2*x2 + 2*x1*x2 - x2, x1^5 - 3*x1^4*x2 - x1^4 + 3*x1^3*x2^2 + 5*x1^3*x2 - x1^2*x2^3 - 7*x1^2*x2^2 - 2*x1^2*x2 + 3*x1*x2^3 + 4*x1*x2^2 - x2^3 - x2^2, x1^3 - x1^2*x2 - x1^2 + 3*x1*x2 - x2, x1^2 - x1*x2 + 2*x2, x1^4 - 3*x1^3*x2 + 3*x1^2*x2^2 + 2*x1^2*x2 - x1*x2^3 - 4*x1*x2^2 + x2^3 + x2^2]