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