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