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 (12*x1^10 - 48*x1^9 + 79*x1^8 - 69*x1^7 + 34*x1^6 - 9*x1^5 + x1^4)
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]