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