The realization space is
  [1   1   0        x1 - 1   1   0    1    1    1         0]
  [1   0   1   2*x1^2 - x1   1   0   x1   x1    0        x1]
  [0   0   0             0   1   1   x1    1   x1   -x1 + 1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (-2*x1^9 + 8*x1^8 - 11*x1^7 + 3*x1^6 + 8*x1^5 - 10*x1^4 + 5*x1^3 - x1^2)
avoiding the zero loci of the polynomials
RingElem[x1^2 - x1 + 1, x1, x1 - 1, 2*x1^2 - 2*x1 + 1, 2*x1 - 1, 2]