The realization space is
  [1   1   0   0   1   1        0                         x1               1                     x1 - 1                         x1]
  [0   1   1   0   0   1   x1 - 1   x1^3 - 2*x1^2 + 2*x1 - 1   x1^2 - x1 + 1   x1^3 - 2*x1^2 + 2*x1 - 1   x1^3 - 2*x1^2 + 2*x1 - 1]
  [0   0   0   1   1   1        1              x1^2 - x1 + 1              x1                       x1^2                       x1^2]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (x1^10 - 5*x1^9 + 12*x1^8 - 20*x1^7 + 24*x1^6 - 21*x1^5 + 13*x1^4 - 5*x1^3 + x1^2)
avoiding the zero loci of the polynomials
RingElem[x1, x1^2 - x1 + 1, x1 - 1, x1^3 - 3*x1^2 + 2*x1 - 1, x1^3 - 2*x1^2 + x1 - 1, x1^2 + 1, 2*x1^2 - 2*x1 + 1, x1^4 - 2*x1^3 + x1 - 1, x1 - 2]