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