The realization space is
  [1   1   0           -3*x1^2 + 3*x1 - 1   0   1   1                    0           -3*x1^2 + 3*x1 - 1         1     x1^2 - 2*x1 + 1]
  [0   1   1   2*x1^3 - 5*x1^2 + 4*x1 - 1   0   0   1            x1^2 - x1   2*x1^3 - 5*x1^2 + 4*x1 - 1   -x1 + 1   2*x1^2 - 3*x1 + 1]
  [0   0   0                            0   1   1   1   -3*x1^2 + 3*x1 - 1        -3*x1^3 + 3*x1^2 - x1        x1        -2*x1^2 + x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (3*x1^14 - 15*x1^13 + 31*x1^12 - 34*x1^11 + 21*x1^10 - 7*x1^9 + x1^8)
avoiding the zero loci of the polynomials
RingElem[x1, 2*x1 - 1, x1 - 1, 3*x1^2 - 3*x1 + 1, 2*x1^2 - 2*x1 + 1, x1^2 - 3*x1 + 1, x1^2 - x1 + 1, 5*x1^3 - 8*x1^2 + 5*x1 - 1]