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   1              x1^3   0   0   1   x1 - 1              x1^3        x1   x1^2 - x1]
  [0   0   0                 0   1   1   1      -x1      -x1^3 + x1^2   -x1 + 1       -x1^2]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (4*x1^12 - 18*x1^11 + 38*x1^10 - 55*x1^9 + 62*x1^8 - 51*x1^7 + 27*x1^6 - 8*x1^5 + x1^4)
avoiding the zero loci of the polynomials
RingElem[2*x1 - 1, x1, x1 - 1, x1^2 + x1 - 1, x1^4 - x1^3 + 4*x1^2 - 4*x1 + 1, x1^4 + 2*x1^2 - 3*x1 + 1, x1^3 - x1^2 + 2*x1 - 1, x1^4 - 2*x1^3 + 5*x1^2 - 4*x1 + 1, x1^3 + 2*x1^2 - 3*x1 + 1, x1^4 - x1^3 + 3*x1^2 - 3*x1 + 1]