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