The realization space is
  [1   1   0           x1 - 1   0   1   1        0           x1 - 1           2*x1 - 1    1]
  [0   1   1   -x1^2 + x1 - 1   0   0   1       x1   -x1^2 + x1 - 1   -x1^2 + 2*x1 - 1   x1]
  [0   0   0                0   1   1   1   x1 - 1        x1^2 - x1               x1^2   x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (2*x1^10 - 10*x1^9 + 22*x1^8 - 27*x1^7 + 19*x1^6 - 7*x1^5 + x1^4)
avoiding the zero loci of the polynomials
RingElem[x1, 2*x1^2 - 2*x1 + 1, 2*x1 - 1, x1 - 1, 3*x1^2 - 3*x1 + 1, x1^2 - x1 + 1, 2*x1^2 - x1 + 1, 2]