The realization space is
  [1   1   0           1   0   1   1         0               x1 - 1         1          x1 - 1]
  [0   1   1   -3*x1 + 2   0   0   1        x1   -3*x1^2 + 5*x1 - 2   -x1 + 1   3*x1^2 - 2*x1]
  [0   0   0           0   1   1   1   -x1 + 1        3*x1^2 - 2*x1        x1   3*x1^2 - 2*x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (-18*x1^7 + 69*x1^6 - 104*x1^5 + 77*x1^4 - 28*x1^3 + 4*x1^2)
avoiding the zero loci of the polynomials
RingElem[x1, 3*x1 - 2, 2*x1 - 1, 3*x1 - 1, x1 - 1, 3*x1^2 - 3*x1 + 1, 6*x1^3 - 8*x1^2 + 4*x1 - 1, 6*x1^2 - 8*x1 + 3, 5*x1^2 - 5*x1 + 1, 5*x1^2 - 6*x1 + 2, 3*x1^2 - 4*x1 + 2]