The realization space is
  [1   1   0        x1^2 - x1 + 1   0   1   1        0        x1^2 - x1 + 1    1      x1 - 1]
  [1   0   1   x1^3 - 2*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     x1^3 - x1^2 + x1   x1        x1^2]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (x1^13 - 6*x1^12 + 14*x1^11 - 15*x1^10 + 24*x1^8 - 38*x1^7 + 33*x1^6 - 18*x1^5 + 6*x1^4 - x1^3)
avoiding the zero loci of the polynomials
RingElem[x1 - 1, x1, 2*x1^2 - 2*x1 + 1, x1^2 - x1 + 1, x1 - 2, x1^3 - 3*x1^2 + 2*x1 - 1, 2*x1 - 1, x1^2 - 2*x1 + 2, x1^3 - x1 + 1, x1^4 - 2*x1^3 + x1 - 1]