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