The realization space is
  [1   1   0   0   1   1        0                  x1^2 - x1      x1 - 1              x1      x1^2 - x1 + 1]
  [1   0   1   0   1   0       x1                       x1^3        x1^2            x1^2               x1^3]
  [0   0   0   1   1   1   x1 - 1   x1^3 - 2*x1^2 + 2*x1 - 1   x1^2 - x1   x1^2 - x1 + 1   x1^3 - x1^2 + x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (-3*x1^8 + 13*x1^7 - 27*x1^6 + 35*x1^5 - 30*x1^4 + 17*x1^3 - 6*x1^2 + x1)
avoiding the zero loci of the polynomials
RingElem[x1 - 1, x1, x1^3 - x1^2 + 2*x1 - 1, x1^2 - x1 + 1, x1^4 - x1^3 + 2*x1^2 - 2*x1 + 1, 2*x1^3 - 2*x1^2 + 2*x1 - 1, x1^2 + 1, 2*x1^2 - 2*x1 + 1, 2*x1 - 1]