The realization space is
  [1   1    1    1    1   0   0    1    1    1]
  [0   1   -1   -1    1   1   0   x1    0   x1]
  [0   1   -1    1   -1   0   1    0   x2   x2]
in the multivariate polynomial ring in 2 variables over ZZ
within the vanishing set of the ideal
Ideal (16*x1^2*x2^2 - 16*x1^2 - 16*x2^2, 16*x1^2*x2^2 - 16*x2^2)
avoiding the zero loci of the polynomials
RingElem[x2, x1, x2 - 1, x2 + 1, x1 - 1, x1 + 1, x1 + x2, 2, x1 - x2, x1*x2 - x1 - x2, x1*x2 + x1 + x2, x1*x2 - x1 + x2, x1*x2 + x1 - x2]