The realization space is
  [1   1   0                       x1^2   0   1   1         0                       x1^2         1                 x1]
  [0   1   1   x1^3 - 2*x1^2 + 3*x1 - 1   0   0   1        x1   x1^3 - 2*x1^2 + 3*x1 - 1        x1               x1^2]
  [0   0   0                          0   1   1   1   -x1 + 1        -x1^3 + 3*x1^2 - x1   -x1 + 1   -x1^2 + 3*x1 - 1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (4*x1^12 - 30*x1^11 + 94*x1^10 - 166*x1^9 + 181*x1^8 - 123*x1^7 + 50*x1^6 - 11*x1^5 + x1^4)
avoiding the zero loci of the polynomials
RingElem[2*x1 - 1, x1, x1 - 1, x1^2 - 3*x1 + 1, x1^4 - 5*x1^3 + 6*x1^2 - 4*x1 + 1, x1^5 - 5*x1^4 + 8*x1^3 - 9*x1^2 + 5*x1 - 1, x1^3 - 2*x1^2 + 3*x1 - 1, x1^3 - 5*x1^2 + 4*x1 - 1, x1^2 - x1 + 1]