The realization space is
  [1   1   0      1   0   1   1          0      1         1    1]
  [0   1   1   2*x1   0   0   1          1   2*x1        x1   x1]
  [0   0   0      0   1   1   1   3*x1 - 2     x1   -x1 + 1   x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (3*x1^2 - 3*x1 + 1, 18*x1^5 - 69*x1^4 + 104*x1^3 - 77*x1^2 + 28*x1 - 4)
avoiding the zero loci of the polynomials
RingElem[x1, 2*x1 - 1, x1 - 1, 3*x1 - 1, 3, 3*x1^2 - 6*x1 + 4, 3*x1^3 - 9*x1^2 + 10*x1 - 3, 9*x1^4 - 30*x1^3 + 36*x1^2 - 17*x1 + 3, 3*x1^2 - 5*x1 + 1, 3*x1^3 - 8*x1^2 + 5*x1 - 1, 3*x1 - 2, 3*x1^3 - 9*x1^2 + 6*x1 - 1, 3*x1^2 - 6*x1 + 2, 3*x1^2 - 4*x1 + 2, 3*x1^2 - 3*x1 - 1, 3*x1^3 - 9*x1^2 + 8*x1 - 3, 3*x1^2 - 2*x1 + 1, 9*x1^4 - 33*x1^3 + 42*x1^2 - 22*x1 + 3, 3*x1^2 - 5*x1 + 3, 9*x1^3 - 24*x1^2 + 21*x1 - 7, 9*x1^4 - 33*x1^3 + 45*x1^2 - 27*x1 + 7, 9*x1^4 - 33*x1^3 + 42*x1^2 - 21*x1 + 4]