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