The realization space is
  [1   1   0   x1^2 - 2*x1 + 1   0   1   1           0             x1^2 - 2*x1 + 1     x1 - 1      x1 - 1]
  [1   0   1         -2*x1 + 1   0   1   0    2*x1 - 1                   -2*x1 + 1   2*x1 - 1    2*x1 - 1]
  [0   0   0                 0   1   1   1   x1^2 - x1   -x1^3 + 3*x1^2 - 3*x1 + 1   2*x1 - 1   x1^2 - x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (-2*x1^12 + 17*x1^11 - 64*x1^10 + 132*x1^9 - 160*x1^8 + 116*x1^7 - 49*x1^6 + 11*x1^5 - x1^4)
avoiding the zero loci of the polynomials
RingElem[x1, x1^2 - 3*x1 + 1, 2*x1 - 1, x1 - 1, x1^3 - 5*x1^2 + 4*x1 - 1, x1 - 2, 3*x1 - 1, x1^3 - 2*x1^2 + 3*x1 - 1, x1^2 + x1 - 1]