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