The realization space is
  [1   0   1   0   1    0     x1^3 - 4*x1^2 + 4*x1   x1^2 - 2*x1     x1^3 - 4*x1^2 + 4*x1     x1^3 - 4*x1^2 + 4*x1               x1 - 2]
  [0   1   1   0   0    1     x1^3 - 4*x1^2 + 4*x1       -x1 + 1         -x1^2 + 3*x1 - 2   x1^3 - 2*x1^2 + x1 - 1   -2*x1^2 + 4*x1 - 1]
  [0   0   0   1   1   -1   x1^3 - x1^2 - 2*x1 + 1            -1   x1^3 - x1^2 - 2*x1 + 1    -x1^3 + x1^2 + x1 + 1          x1^2 - 2*x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (x1^4 - 3*x1^3 + 3*x1^2 - x1 - 1)
avoiding the zero loci of the polynomials
RingElem[2*x1^2 - 3*x1 - 1, x1 - 1, x1, x1^3 - 2*x1^2 + x1 - 1, x1^2 - x1 + 1, x1^2 - x1 - 1, x1 - 2, x1^3 - 3*x1^2 + 4*x1 - 3, x1^4 - 3*x1^3 + 4*x1^2 - 4*x1 + 1, 2*x1^3 - 5*x1^2 + 3*x1 - 1, 2*x1^5 - 8*x1^4 + 11*x1^3 - 7*x1^2 + 2*x1 + 1, 2*x1^5 - 9*x1^4 + 16*x1^3 - 16*x1^2 + 9*x1 - 1, 2*x1^2 - 4*x1 + 1, x1^7 - 7*x1^6 + 21*x1^5 - 33*x1^4 + 27*x1^3 - 11*x1^2 + 2*x1 + 1, x1^7 - 7*x1^6 + 22*x1^5 - 39*x1^4 + 40*x1^3 - 23*x1^2 + 6*x1 + 1, x1^4 - 4*x1^3 + 6*x1^2 - 3*x1 - 1, x1^3 - x1^2 - x1 - 1, 2*x1^5 - 9*x1^4 + 15*x1^3 - 12*x1^2 + 4*x1 + 1, 2*x1^5 - 8*x1^4 + 12*x1^3 - 11*x1^2 + 6*x1 + 1, 2*x1^6 - 10*x1^5 + 20*x1^4 - 22*x1^3 + 13*x1^2 - x1 - 1, 2*x1^4 - 6*x1^3 + 7*x1^2 - 4*x1 - 1, 2*x1^4 - 6*x1^3 + 6*x1^2 - 2*x1 - 1, 2*x1^3 - 4*x1^2 + 1]