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