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