The realization space is
  [1   1             x2             x2   0             x2   0   x2   x2    0    1]
  [1   0   x1*x2^2 + x3   x1*x2^2 + x3   1           x2^2   0   x2    0    1   x2]
  [1   0   x1*x2^2 + x3             x2   0   x1*x2^2 + x3   1   x3   x3   x1   x3]
in the multivariate polynomial ring in 3 variables over ZZ
within the vanishing set of the ideal
Ideal with 3 generators
avoiding the zero loci of the polynomials
RingElem[x1*x2 - x1 - x3 + 1, x1*x2 - x3, x1^2*x2^2 - 2*x1*x2^2 + x1*x3 + x2*x3 - x3, x1^2*x2^2 - x1*x2^2 + x1*x3 + x2*x3 - x2, x1, x1*x2^2 - x2*x3 + x3, x2 - 1, x2^2 - 2*x2*x3 + x3, x3, x2, x1*x2^4 - x1*x2^3*x3 + x1*x2^2*x3 - x2*x3^2 + x3^2, x1*x2^3*x3 - x1*x2^2*x3 - x2^3 + x2^2*x3 + x2*x3^2 - x3^2, x2 - x3, x1*x2^2 + x3, x1*x2^2*x3 - x2^2 + x3^2, x1*x2^2 - x2^2 + x3, x3 - 1, x1*x2^2 - x2 + x3, x1*x2 - x2 + x3, x1^2*x2^2 + x1*x3 - x2 + x3, x1*x2^2 - x2^2 - x2 + x3, x1^2*x2^2 - x1*x2 + x1*x3 - x2 + x3, x1^2*x2^2 + x1*x3 - x2, x1 - 1, x1^2*x2^3 - x1*x2^2 + x1*x2*x3 - x2^2 + x2*x3 + x2 - x3]