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