The realization space is
  [1   1   0   1   0   0   x1    1          x2 - x3         x2 - x3    1]
  [0   1   1   1   1   0   x2   x2    -x1*x2 + x2^2   -x1*x2 + x2^2   x2]
  [0   0   0   1   1   1   x1   x1   -x1*x3 + x2*x3   x1*x2 - x1*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*x3 - x1*x2^2 - 2*x1*x2*x3 + x1*x2 - x1*x3 + x2^2*x3)
avoiding the zero loci of the polynomials
RingElem[x1 - x3, x2, x2^2 - x2 + x3, x2^2 - 2*x2 + x3, 2*x2 - x3, x1*x2 - x1 - x2 + x3, x3, x2 - 1, x1 - 1, x1*x2 + x1*x3 - x1 - x2*x3, x3 - 1, x1 - x2, x1*x2 - x1*x3 + x1 - x2, x2 - x3, x2 - x3 - 1, x1*x2 - x2^2 + x2 - x3, x1^2 - x1*x2 + x2 - x3, x1, x1*x3 - x2*x3 + x2 - x3, 2*x1^2*x2 - x1^2*x3 - x1*x2^2 - x1*x2 + x1*x3 + x2^2 - x2*x3, 2*x1*x2 - x1*x3 - x2^2, 2*x1*x2 - x1*x3 - x2^2 + x2 - x3, x1 - x2 + 1, 2*x1 - x2]