The realization space is
  [1   1   0               x1 - 1   0   1   1        0               x1 - 1         1    1]
  [0   1   1   -2*x1^2 + 2*x1 - 1   0   0   1       x1   -2*x1^2 + 2*x1 - 1   -x1 + 1   x1]
  [0   0   0                    0   1   1   1   x1 - 1        2*x1^2 - 2*x1        x1   x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (32*x1^11 - 216*x1^10 + 616*x1^9 - 974*x1^8 + 938*x1^7 - 566*x1^6 + 210*x1^5 - 44*x1^4 + 4*x1^3)
avoiding the zero loci of the polynomials
RingElem[x1, 2*x1 - 1, x1 - 1, 4*x1^2 - 5*x1 + 2, 2, 3*x1^2 - 3*x1 + 1, 4*x1^2 - 3*x1 + 1, 2*x1^2 - 2*x1 + 1, 4*x1^2 - 2*x1 + 1, 4*x1 - 1]