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                x1   0   1   0           2*x1 - 1                x1      -x1         -x1]
  [0   0   0                 0   1   1   1   -x1^2 + 2*x1 - 1        -x1^2 + x1      -x1   x1^2 - x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (6*x1^13 - 37*x1^12 + 97*x1^11 - 140*x1^10 + 120*x1^9 - 61*x1^8 + 17*x1^7 - 2*x1^6)
avoiding the zero loci of the polynomials
RingElem[2*x1 - 1, x1, x1 - 1, x1^2 - 3*x1 + 1, x1^2 - x1 + 1, x1^2 + x1 - 1, x1^3 + 2*x1^2 - 3*x1 + 1, 3*x1 - 1, x1^3 - 2*x1^2 + 3*x1 - 1, 3*x1^2 - 3*x1 + 1, 2*x1^2 - 4*x1 + 1, x1^2 - 4*x1 + 2]