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