The realization space is
  [1   1   0           x1^2 - x1   0   1   1        0            x1^3 - x1^2         1                 x1]
  [0   1   1   2*x1^2 - 2*x1 + 1   0   0   1   x1 - 1   2*x1^3 - 2*x1^2 + x1   -x1 + 1   -x1^2 + 2*x1 - 1]
  [0   0   0                   0   1   1   1      -x1        x1^2 - 2*x1 + 1        x1               x1^2]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (2*x1^11 - 4*x1^10 - 2*x1^9 + 19*x1^8 - 35*x1^7 + 35*x1^6 - 21*x1^5 + 7*x1^4 - x1^3)
avoiding the zero loci of the polynomials
RingElem[x1, x1 - 1, x1^3 - x1 + 1, 2*x1^5 - x1^4 - 3*x1^3 + 6*x1^2 - 4*x1 + 1, x1^2 - x1 + 1, x1^3 + x1^2 - 2*x1 + 1, x1^4 + x1^3 - 3*x1^2 + 3*x1 - 1, 2*x1^2 - 2*x1 + 1, 2*x1 - 1, x1^4 - 2*x1^2 + 3*x1 - 1]