The realization space is
  [1   1   0   0   1   1                 0                 1                     x1 - 1                           x1^2 - x1                         x1]
  [0   1   1   0   0   1   x1^2 - 2*x1 + 1   x1^2 - 2*x1 + 1   x1^3 - 2*x1^2 + 2*x1 - 1   x1^4 - 3*x1^3 + 4*x1^2 - 3*x1 + 1   x1^3 - 2*x1^2 + 2*x1 - 1]
  [0   0   0   1   1   1                x1                x1                       x1^2                                x1^3                       x1^2]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (-2*x1^11 + 10*x1^10 - 23*x1^9 + 34*x1^8 - 35*x1^7 + 26*x1^6 - 14*x1^5 + 5*x1^4 - x1^3)
avoiding the zero loci of the polynomials
RingElem[x1 - 1, x1^2 - x1 + 1, x1, x1^3 - 2*x1^2 + x1 - 1, x1^3 - 3*x1^2 + 2*x1 - 1, x1 - 2, x1^2 + 1, x1^4 - 3*x1^3 + 3*x1^2 - 3*x1 + 1, x1^4 - 4*x1^3 + 4*x1^2 - 3*x1 + 1, x1^2 - 3*x1 + 1]