The realization space is
  [1   1   0        x1 - 1   0   1   1         0             x1 - 1         1    1]
  [0   1   1   2*x1^2 - x1   0   0   1        x1        2*x1^2 - 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 (4*x1^11 - 16*x1^10 + 25*x1^9 - 19*x1^8 + 7*x1^7 - x1^6)
avoiding the zero loci of the polynomials
RingElem[x1, 2*x1 - 1, x1 - 1, 3*x1^2 - 3*x1 + 1, 3*x1^3 - 5*x1^2 + 4*x1 - 1, 3*x1 - 1, 2*x1^2 - 2*x1 + 1, 2, x1^2 - x1 + 1]