The realization space is
  [1   1   0   0   1   1           0      x1 - 1   -2*x1^2 + 3*x1 - 1   -2*x1^2 + 3*x1 - 1      x1^2 - 2*x1 + 1]
  [1   0   1   0   1   0   -2*x1 + 1         -x1          2*x1^2 - x1                 x1^2         -2*x1^2 + x1]
  [0   0   0   1   1   1   x1^2 - x1   x1^2 - x1         -x1^3 + x1^2         -x1^3 + x1^2   x1^3 - 2*x1^2 + x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (6*x1^12 - 21*x1^11 + 17*x1^10 + 28*x1^9 - 72*x1^8 + 68*x1^7 - 34*x1^6 + 9*x1^5 - x1^4)
avoiding the zero loci of the polynomials
RingElem[3*x1^2 - 3*x1 + 1, x1, x1^3 + 2*x1^2 - 3*x1 + 1, x1^3 - 5*x1^2 + 4*x1 - 1, 2*x1 - 1, x1 - 1, x1^3 - 4*x1^2 + 3*x1 - 1, x1^2 + x1 - 1, x1^2 - 3*x1 + 1]