The realization space is
  [1   1   0   x1^2 - 2*x1 + 1   0   1   1        0      x1^2 - 2*x1 + 1    1                x1]
  [1   0   1              x1^3   0   1   0       x1                 x1^3   x1              x1^2]
  [0   0   0                 0   1   1   1   x1 - 1   x1^3 - 2*x1^2 + x1   x1   x1^2 - 2*x1 + 1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (x1^13 - 4*x1^12 + 8*x1^11 - 15*x1^10 + 26*x1^9 - 30*x1^8 + 20*x1^7 - 7*x1^6 + x1^5)
avoiding the zero loci of the polynomials
RingElem[x1 - 1, 2*x1 - 1, x1, x1^3 - x1^2 + 2*x1 - 1, x1^2 - 3*x1 + 1, x1^3 - 2*x1^2 - x1 + 1, x1^5 - 3*x1^4 + 3*x1^3 - 5*x1^2 + 4*x1 - 1, x1^2 + x1 - 1, x1^2 - x1 + 1, x1^3 + x1 - 1]