The realization space is
  [1   1   0   -x1^2 + 2*x1 - 1   0   1   1         0           -x1^2 + 2*x1 - 1         1                 x1]
  [0   1   1              -x1^3   0   0   1        x1                      -x1^3        x1               x1^2]
  [0   0   0                  0   1   1   1   -x1 + 1   x1^3 - 3*x1^2 + 3*x1 - 1   -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 (-2*x1^11 + 15*x1^10 - 49*x1^9 + 95*x1^8 - 125*x1^7 + 118*x1^6 - 79*x1^5 + 35*x1^4 - 9*x1^3 + x1^2)
avoiding the zero loci of the polynomials
RingElem[2*x1 - 1, x1, x1 - 1, x1^3 - 2*x1^2 + 3*x1 - 1, x1^2 - 3*x1 + 1, x1^3 - x1^2 + 2*x1 - 1, x1^4 - 2*x1^3 + 5*x1^2 - 4*x1 + 1, x1^2 + x1 - 1, x1^2 - x1 + 1]