The realization space is
  [1   1   0   x1 - 1   0   1   1                  0             x1 - 1         1    1]
  [0   1   1    -x1^2   0   0   1        2*x1^2 - x1              -x1^2        x1   x1]
  [0   0   0        0   1   1   1   -x1^2 + 2*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 (-8*x1^9 + 28*x1^8 - 30*x1^7 - 3*x1^6 + 30*x1^5 - 24*x1^4 + 8*x1^3 - x1^2)
avoiding the zero loci of the polynomials
RingElem[x1, 2*x1 - 1, x1 - 1, 3*x1 - 2, 3*x1^2 - 3*x1 + 1, 3*x1^3 - 4*x1^2 + 3*x1 - 1, x1^2 + x1 - 1, x1^3 + 2*x1^2 - 3*x1 + 1, 3*x1 - 1, 3*x1^2 - 1, 3*x1^3 - x1^2 - 2*x1 + 1]