The realization space is
  [1   1   0          x1 - 1   0   1   1         0             x1 - 1         1    1]
  [0   1   1   3*x1^2 - 2*x1   0   0   1        x1      3*x1^2 - 2*x1        x1   x1]
  [0   0   0               0   1   1   1   -x1 + 1   -x1^2 + 2*x1 - 1   -x1 + 1   x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (-18*x1^8 + 84*x1^7 - 165*x1^6 + 178*x1^5 - 115*x1^4 + 45*x1^3 - 10*x1^2 + x1)
avoiding the zero loci of the polynomials
RingElem[x1, 2*x1 - 1, x1 - 1, 2*x1^2 - 2*x1 + 1, 2, 3*x1 - 2, 3*x1 - 1, 3*x1^2 - 3*x1 + 1, 3*x1^3 - 4*x1^2 + 3*x1 - 1, 3]