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