The realization space is
  [1                x2   1   1   0    1   0   x2                x2    1    1]
  [1   x1*x2 - x1 + x2   0   0   1   x1   0   x2   x1*x2 - x1 + x2   x1   x2]
  [1   x1*x2 - x1 + x2   0   1   0    0   1   x3                x3   x3   x3]
in the multivariate polynomial ring in 3 variables over ZZ
within the vanishing set of the ideal
Ideal (x1^2*x2 - x1^2 + x1*x2 - x1 + x2)
avoiding the zero loci of the polynomials
RingElem[x3 - 1, x1 - x2, x1*x2 - x1 - x2*x3 + x2, x3, x2 - 1, x1*x3 - x1 + x2 - x3, x1*x2 - x1 + x2 - x3, x1, x1*x3 - x1 + x2, x2 - x3, x1*x2 - x1 + x2, x2, x1*x2^2 - x1*x2*x3 + x1*x3 - x1 - x2*x3 + x2, x1*x2*x3 - 2*x1*x3 + x1 - x2 + x3, x1*x2 - 2*x1 + x2, x1*x2*x3 - 2*x1*x3 + x1 + x2*x3 - x2, x1 - 1, x1^2*x2^2 - x1^2*x2 - x1*x2^2*x3 + x1*x2*x3 + x1*x2 - x1*x3 - x2^2 + x2*x3, x1*x2 - x1*x3 + x2*x3 - x2, x1^2*x2 - x1^2 - x1*x2*x3 + x1*x2 + x1*x3 - x1 - x2*x3 + x2, x1 - x3, x1^2*x2^2 - x1^2*x2 + x1*x2 - x1*x3 - x2^2 + x2*x3, x1*x2 - x1*x3 - x2, 2*x1*x2^2 - x1*x2*x3 - 2*x1*x2 + x1*x3 + x2^2 - x2*x3]