The realization space is
  [1   1   0                x1   0   1   1          0                x1         1         1]
  [1   0   1   x1^2 - 2*x1 + 1   0   1   0   2*x1 - 1   x1^2 - 2*x1 + 1   -x1 + 1   -x1 + 1]
  [0   0   0                 0   1   1   1         x1        -x1^2 + x1   -x1 + 1        x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (12*x1^9 - 68*x1^8 + 155*x1^7 - 186*x1^6 + 128*x1^5 - 51*x1^4 + 11*x1^3 - x1^2)
avoiding the zero loci of the polynomials
RingElem[x1, 2*x1 - 1, x1 - 1, 3*x1 - 2, 3*x1 - 1, 3*x1^2 - 3*x1 + 1, x1^2 - 3*x1 + 1, x1^3 - 5*x1^2 + 4*x1 - 1, 3*x1^2 - 6*x1 + 2]