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