The realization space is
  [1   0   1   1   0   1                         2                      1                         2                         2      1]
  [0   1   1   0   0   1   6*x1*x2 - 3*x1 - x2 + 2   -6*x1*x2 + 3*x1 + x2   -12*x1*x2 + 6*x1 + 2*x2   6*x1*x2 - 3*x1 - x2 + 2   2*x2]
  [0   0   0   1   1   1      -6*x1*x2 + 3*x1 + x2                     x1      -6*x1*x2 + 3*x1 + x2                      2*x1     x2]
in the multivariate polynomial ring in 2 variables over ZZ
within the vanishing set of the ideal
Ideal with 2 generators
avoiding the zero loci of the polynomials
RingElem[6*x1*x2 - 7*x1 - x2 + 2, x2, x1 - x2, 6*x1*x2^2 - 13*x1*x2 + 3*x1 - x2^2 + 7*x2 - 2, 6*x1*x2 - 3*x1 - 5*x2 + 2, 6*x1*x2^2 - 13*x1*x2 + 5*x1 - x2^2 + 5*x2 - 2, 6*x1*x2 - x1 - x2, 18*x1*x2 - 9*x1 - 3*x2 + 2, 6*x1*x2 - 3*x1 + x2, 2, 6*x1*x2^2 - x1*x2 - x1 - x2^2 + x2, 6*x1*x2^2 - 7*x1*x2 + 3*x1 - x2^2 - x2, 18*x1^2*x2^2 - 21*x1^2*x2 + 6*x1^2 + 9*x1*x2^2 - 2*x1*x2 - x1 - 2*x2^2 + x2, 6*x1*x2 - 3*x1 - x2, 3*x2 - 1, 6*x1*x2 - 3*x1 - x2 + 2, 18*x1*x2^2 - 21*x1*x2 + 6*x1 - 3*x2^2 + 6*x2 - 2, x2 - 1, 2*x2 - 1, 36*x1^2*x2^2 - 60*x1^2*x2 + 21*x1^2 - 12*x1*x2^2 + 10*x1*x2 - 4*x1 + x2^2, 36*x1^2*x2^2 - 60*x1^2*x2 + 21*x1^2 - 12*x1*x2^2 + 58*x1*x2 - 24*x1 + x2^2 - 8*x2 + 4, 36*x1^2*x2^2 - 60*x1^2*x2 + 21*x1^2 - 12*x1*x2^2 + 46*x1*x2 - 22*x1 + x2^2 - 6*x2 + 4, x1, x1 - 1, 6*x1*x2 - 5*x1 - x2 + 2, 6*x1*x2 - 3*x1 - x2 + 1, 6*x1*x2 - 4*x1 - x2 + 1, 36*x1^2*x2^2 - 42*x1^2*x2 + 12*x1^2 - 12*x1*x2^2 + 31*x1*x2 - 12*x1 + x2^2 - 4*x2 + 2, 6*x1*x2 - 2*x1 - x2]