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