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