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