The realization space is
  [1   1   0   0   1   1                          0                  x1^2 - x1     x1^2 - 2*x1 + 1      x1^2 - 2*x1 + 1           x1^2 - x1]
  [0   1   1   0   0   1   x1^3 - 2*x1^2 + 2*x1 - 1   x1^3 - 2*x1^2 + 2*x1 - 1         x1^3 - x1^2   x1^3 - 2*x1^2 + x1         x1^3 - x1^2]
  [0   0   0   1   1   1          2*x1^2 - 2*x1 + 1          2*x1^2 - 2*x1 + 1   2*x1^2 - 2*x1 + 1    2*x1^2 - 2*x1 + 1   2*x1^2 - 2*x1 + 1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (-4*x1^9 + 24*x1^8 - 68*x1^7 + 120*x1^6 - 145*x1^5 + 124*x1^4 - 75*x1^3 + 31*x1^2 - 8*x1 + 1)
avoiding the zero loci of the polynomials
RingElem[x1, 2*x1^2 - 2*x1 + 1, x1 - 1, x1^3 - 3*x1^2 + 2*x1 - 1, x1^2 - x1 + 1, x1^3 + x1^2 - x1 + 1, x1^4 - 2*x1^3 + x1 - 1, x1^3 - x1 + 1, x1^4 - 5*x1^3 + 6*x1^2 - 4*x1 + 1, x1^3 - 4*x1^2 + 3*x1 - 1, x1^3 - 4*x1^2 + 4*x1 - 2]