The realization space is
  [1   0   1             2*x1 - 1   1   0          1   1         1   0             2*x1 - 1]
  [0   1   1   -3*x1^2 + 4*x1 - 1   0   0          0   1   -x1 + 1   1   -3*x1^2 + 4*x1 - 1]
  [0   0   0                    0   1   1   3*x1 - 1   1        x1   1          3*x1^2 - x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (6*x1^5 - 21*x1^4 + 25*x1^3 - 12*x1^2 + 2*x1)
avoiding the zero loci of the polynomials
RingElem[x1, 3*x1 - 1, 2*x1 - 1, 3, 3*x1 - 2, x1 - 1, 3*x1^2 - 3*x1 + 1, 2, 3*x1^2 - 6*x1 + 2]