The realization space is
  [1   1   0   0   1   1                   0   x1^3 - 3*x1^2 + 3*x1 - 1   x1^2 - 2*x1 + 1   x1^3 - 3*x1^2 + 3*x1 - 1        x1 - 1]
  [0   1   1   0   0   1   2*x1^2 - 3*x1 + 1      -2*x1^3 + 3*x1^2 - x1        -x1^2 + x1        -x1^3 + 2*x1^2 - x1     x1^2 - x1]
  [0   0   0   1   1   1   3*x1^2 - 3*x1 + 1      -3*x1^3 + 3*x1^2 - x1      -2*x1^2 + x1      -3*x1^3 + 3*x1^2 - x1   2*x1^2 - x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (28*x1^14 - 142*x1^13 + 318*x1^12 - 413*x1^11 + 341*x1^10 - 183*x1^9 + 62*x1^8 - 12*x1^7 + x1^6)
avoiding the zero loci of the polynomials
RingElem[x1, 2*x1^2 - 2*x1 + 1, 2*x1 - 1, x1 - 1, 3*x1^2 - 3*x1 + 1, x1^3 + 2*x1^2 - 3*x1 + 1, 5*x1^4 - 10*x1^3 + 10*x1^2 - 5*x1 + 1, 5*x1^3 - 8*x1^2 + 5*x1 - 1, 5*x1^2 - 6*x1 + 2]