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