The realization space is
  [1   1   x1 - 1   0   0   1   x1^2 - x1 + 1   x1^2 - 2*x1 + 1               0   x1^2 - 2*x1 + 1      x1^2 - x1 + 1]
  [1   0     x1^2   1   0   1               0       x1^3 - x1^2   x1^2 - x1 + 1              x1^2   x1^3 - x1^2 + x1]
  [0   0        0   0   1   1            x1^2              x1^2              x1              x1^2               x1^2]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (x1^12 - 6*x1^11 + 14*x1^10 - 21*x1^9 + 20*x1^8 - 13*x1^7 + 5*x1^6 - x1^5)
avoiding the zero loci of the polynomials
RingElem[x1, x1 - 2, x1 - 1, x1^3 - 4*x1^2 + 3*x1 - 1, x1^2 - 3*x1 + 1, 2*x1 - 1, x1 + 1, x1^2 - x1 + 1]