The realization space is
  [1   1   0               x1 - 1   0   1   1        0               x1^2 - 2*x1 + 1         1    1]
  [0   1   1   -2*x1^2 + 2*x1 - 1   0   0   1       x1   -2*x1^3 + 4*x1^2 - 3*x1 + 1   -x1 + 1   x1]
  [0   0   0                    0   1   1   1   x1 - 1          2*x1^3 - 2*x1^2 + x1        x1   x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (8*x1^9 - 38*x1^8 + 79*x1^7 - 93*x1^6 + 67*x1^5 - 30*x1^4 + 8*x1^3 - x1^2)
avoiding the zero loci of the polynomials
RingElem[x1, 2*x1 - 1, x1 - 1, 2*x1^2 - 2*x1 + 1, 4*x1^2 - 3*x1 + 1, 3*x1^2 - 3*x1 + 1, 4*x1^4 - 9*x1^3 + 10*x1^2 - 5*x1 + 1, 2, 4*x1^3 - 7*x1^2 + 5*x1 - 1, 2*x1^2 - 3*x1 + 2, x1^2 - x1 + 1]