The realization space is
  [1   1   0   x1^2 - x1 + 1   0   1   1        0   x1^3 - 2*x1^2 + 2*x1 - 1    1      x1 - 1]
  [1   0   1      -x1^2 + x1   0   1   0   x1 - 1        -x1^3 + 2*x1^2 - x1   x1   x1^2 - x1]
  [0   0   0               0   1   1   1       x1         x1^4 - x1^3 + x1^2   x1        x1^2]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (2*x1^13 - 14*x1^12 + 41*x1^11 - 72*x1^10 + 84*x1^9 - 67*x1^8 + 36*x1^7 - 12*x1^6 + 2*x1^5)
avoiding the zero loci of the polynomials
RingElem[x1 - 1, x1, x1^2 - x1 + 1, 2*x1^2 - 2*x1 + 1, x1^3 + x1^2 - x1 + 1, x1^3 - x1 + 1, x1^3 - x1^2 + 1, 2*x1 - 1, x1^4 + x1^2 - x1 + 1, x1^4 - x1^3 + 2*x1^2 - 2*x1 + 1, x1^4 - 3*x1^3 + 5*x1^2 - 3*x1 + 1]