The realization space is
  [1   1   0    4*x1^2 - 4*x1 + 1   0   1   1          0      4*x1^2 - 4*x1 + 1    2*x1 - 1      2*x1 - 1]
  [1   0   1   x1^3 - 2*x1^2 + x1   0   1   0         x1     x1^3 - 2*x1^2 + x1   x1^2 - x1     x1^2 - x1]
  [0   0   0                    0   1   1   1   2*x1 - 1   2*x1^3 - 3*x1^2 + x1   x1^2 - x1   2*x1^2 - x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (12*x1^11 - 92*x1^10 + 291*x1^9 - 480*x1^8 + 452*x1^7 - 251*x1^6 + 81*x1^5 - 14*x1^4 + x1^3)
avoiding the zero loci of the polynomials
RingElem[x1^2 - 3*x1 + 1, x1 - 1, x1, 2*x1 - 1, 3*x1 - 1, x1^3 - 5*x1^2 + 4*x1 - 1, x1^3 - 6*x1^2 + 5*x1 - 1, 2*x1^2 - 4*x1 + 1, 5*x1^2 - 5*x1 + 1, 3*x1^3 - 9*x1^2 + 6*x1 - 1]