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