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