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