The realization space is
  [1   1   0                 1   0   1   1           0                 1    1         1]
  [1   0   1   -3*x1*x2 + 2*x1   0   1   0           1   -3*x1*x2 + 2*x1   x1   -x2 + 1]
  [0   0   0                 0   1   1   1   -3*x2 + 2                x1   x1        x2]
in the multivariate polynomial ring in 2 variables over ZZ
within the vanishing set of the ideal
Ideal (3*x2^2 - 3*x2 + 1)
avoiding the zero loci of the polynomials
RingElem[x2, 2*x1 - 1, x1, 2*x2 - 1, x1 - x2, 3*x1*x2 - 2*x1 - 3*x2^2 + 1, x1 + x2 - 1, x1 - 1, x2 - 1, 3*x1*x2 - x1 + 3*x2^2 - 6*x2 + 2, 3*x2 - 1, 3*x1*x2 - 3*x1 + 1, 3*x1*x2 - 2*x1 - x2 + 1, 3*x1*x2^2 - 6*x1*x2 + 2*x1 + 2*x2 - 1, 9*x1*x2^2 - 12*x1*x2 + 3*x1 - 3*x2^2 + 6*x2 - 2, 3, 3*x2^2 - 6*x2 + 2, 3*x2 - 2, 9*x1*x2^2 - 12*x1*x2 + 4*x1 - 3*x2^2 + 6*x2 - 2, 3*x1*x2 - 2*x1 + 1, 3*x1*x2^2 - 5*x1*x2 + 2*x1 + 2*x2 - 1, 3*x1*x2 - x1 - 3*x2 + 2, 3*x1*x2 - x1 - 1, 3*x1*x2 - 2*x1 - 3*x2 + 1, 9*x1*x2^2 - 12*x1*x2 + 3*x1 + 3*x2 - 2, 9*x1*x2^2 - 12*x1*x2 + 3*x1 + 1, 9*x1*x2^2 - 12*x1*x2 + 4*x1 + 1, 9*x1*x2^2 - 12*x1*x2 + 4*x1 + 3*x2 - 1]