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