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