The realization space is
  [1   0   1   -x1 + 1   0   1      x1^2    0        x1   -x1 + 1          x1]
  [0   1   1         1   0   0         0    1        x1        x1        x1^2]
  [0   0   0         0   1   1   -x1 + 1   -1   -x1 + 1   -x1 + 1   -x1^2 + 1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (2*x1^9 - 3*x1^8 - 9*x1^7 + 27*x1^6 - 27*x1^5 + 12*x1^4 - 2*x1^3)
avoiding the zero loci of the polynomials
RingElem[x1 - 1, x1^2 + x1 - 1, x1^2 + 2*x1 - 1, 2*x1 - 1, x1, x1^3 + x1 - 1, x1^2 - x1 + 1, x1 + 1]