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