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