The realization space is
  [1   1   0   -2*x1^2 + 3*x1 - 1   0   1   1          0   -2*x1^2 + 3*x1 - 1   x1 - 1          -2*x1 + 1]
  [1   0   1      x1^2 + 2*x1 - 1   0   1   0         x1      x1^2 + 2*x1 - 1      -x1   -x1^2 - 2*x1 + 1]
  [0   0   0                    0   1   1   1   2*x1 - 1          2*x1^2 - x1      -x1       -2*x1^2 + x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (8*x1^8 - 40*x1^7 + 66*x1^6 - 48*x1^5 + 16*x1^4 - 2*x1^3)
avoiding the zero loci of the polynomials
RingElem[x1, 3*x1 - 1, x1^2 - 3*x1 + 1, 2*x1 - 1, x1^3 + 3*x1^2 - 4*x1 + 1, x1 - 1, x1^2 + 2*x1 - 1, 5*x1 - 2, 2]