The realization space is
  [1   1   0                  x1   0   1   1        0                  x1         1    1]
  [0   1   1   3*x1^2 - 3*x1 + 1   0   0   1   x1 - 1   3*x1^2 - 3*x1 + 1        x1   x1]
  [0   0   0                   0   1   1   1      -x1          -x1^2 + x1   -x1 + 1   x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (6*x1^8 - 17*x1^7 + 21*x1^6 - 15*x1^5 + 6*x1^4 - x1^3)
avoiding the zero loci of the polynomials
RingElem[x1, 2*x1 - 1, x1 - 1, 2, 2*x1^2 - 2*x1 + 1, 3*x1^2 - 3*x1 + 1, 3*x1^3 - 5*x1^2 + 4*x1 - 1, 3*x1 - 1, 3*x1 - 2, 3*x1^2 - 4*x1 + 2]