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