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